diff --git a/moto/cognitoidp/models.py b/moto/cognitoidp/models.py
--- a/moto/cognitoidp/models.py
+++ b/moto/cognitoidp/models.py
@@ -1270,8 +1270,8 @@ def admin_initiate_auth(self, user_pool_id, client_id, auth_flow, auth_parameter
         elif auth_flow is AuthFlow.REFRESH_TOKEN:
             refresh_token = auth_parameters.get("REFRESH_TOKEN")
             (
-                id_token,
                 access_token,
+                id_token,
                 expires_in,
             ) = user_pool.create_tokens_from_refresh_token(refresh_token)
 

Thanks for raising this @lkw225657!
diff --git a/tests/test_cognitoidp/test_cognitoidp.py b/tests/test_cognitoidp/test_cognitoidp.py
--- a/tests/test_cognitoidp/test_cognitoidp.py
+++ b/tests/test_cognitoidp/test_cognitoidp.py
@@ -3939,6 +3939,41 @@ def test_admin_reset_password_and_change_password():
     result["UserStatus"].should.equal("CONFIRMED")
 
 
+@mock_cognitoidp
+def test_admin_initiate_auth__use_access_token():
+    client = boto3.client("cognito-idp", "us-west-2")
+    un = str(uuid.uuid4())
+    pw = str(uuid.uuid4())
+    # Create pool and client
+    user_pool_id = client.create_user_pool(PoolName=str(uuid.uuid4()))["UserPool"]["Id"]
+    client_id = client.create_user_pool_client(
+        UserPoolId=user_pool_id, ClientName=str(uuid.uuid4()), GenerateSecret=True
+    )["UserPoolClient"]["ClientId"]
+    client.admin_create_user(UserPoolId=user_pool_id, Username=un, TemporaryPassword=pw)
+    client.confirm_sign_up(ClientId=client_id, Username=un, ConfirmationCode="123456")
+
+    # Initiate once, to get a refresh token
+    auth_result = client.admin_initiate_auth(
+        UserPoolId=user_pool_id,
+        ClientId=client_id,
+        AuthFlow="ADMIN_NO_SRP_AUTH",
+        AuthParameters={"USERNAME": un, "PASSWORD": pw},
+    )
+    refresh_token = auth_result["AuthenticationResult"]["RefreshToken"]
+
+    # Initiate Auth using a Refresh Token
+    auth_result = client.admin_initiate_auth(
+        UserPoolId=user_pool_id,
+        ClientId=client_id,
+        AuthFlow="REFRESH_TOKEN",
+        AuthParameters={"REFRESH_TOKEN": refresh_token},
+    )
+    access_token = auth_result["AuthenticationResult"]["AccessToken"]
+
+    # Verify the AccessToken of this authentication works
+    client.global_sign_out(AccessToken=access_token)
+
+
 @mock_cognitoidp
 def test_admin_reset_password_disabled_user():
     client = boto3.client("cognito-idp", "us-west-2")

cognito-idp admin_initiate_auth can't refresh token
## Reporting Bugs
moto==3.1.6
/moto/cognitoidp/[models.py](https://github.com/spulec/moto/tree/9a8c9f164a472598d78d30c78f4581810d945995/moto/cognitoidp/models.py)
function admin_initiate_auth line:1276

        elif auth_flow is AuthFlow.REFRESH_TOKEN:
            refresh_token = auth_parameters.get("REFRESH_TOKEN")
            (
                id_token,
                access_token,
                expires_in,
            ) = user_pool.create_tokens_from_refresh_token(refresh_token)

id_token and access_token is in the opposite position

It is different from other call create_tokens_from_refresh_token

function initiate_auth line:1681

            if client.generate_secret:
                secret_hash = auth_parameters.get("SECRET_HASH")
                if not check_secret_hash(
                    client.secret, client.id, username, secret_hash
                ):
                    raise NotAuthorizedError(secret_hash)

            (
                access_token,
                id_token,
                expires_in,
            ) = user_pool.create_tokens_from_refresh_token(refresh_token)




tests/test_cognitoidp/test_cognitoidp.py::test_admin_initiate_auth__use_access_token
tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_custom_attribute_required tests/test_cognitoidp/test_cognitoidp.py::test_admin_confirm_sign_up tests/test_cognitoidp/test_cognitoidp.py::test_get_user_unknown_accesstoken tests/test_cognitoidp/test_cognitoidp.py::test_update_user_pool tests/test_cognitoidp/test_cognitoidp.py::test_global_sign_out tests/test_cognitoidp/test_cognitoidp.py::test_list_identity_providers_when_max_items_more_than_total_items tests/test_cognitoidp/test_cognitoidp.py::test_admin_create_user_with_username_attributes tests/test_cognitoidp/test_cognitoidp.py::test_group_in_access_token tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_invalid_schema_values[invalid_max_value] tests/test_cognitoidp/test_cognitoidp.py::test_list_user_pools_returns_next_tokens tests/test_cognitoidp/test_cognitoidp.py::test_user_authentication_flow tests/test_cognitoidp/test_cognitoidp.py::test_admin_remove_user_from_group_again_is_noop tests/test_cognitoidp/test_cognitoidp.py::test_idtoken_contains_kid_header tests/test_cognitoidp/test_cognitoidp.py::test_admin_list_groups_for_user tests/test_cognitoidp/test_cognitoidp.py::test_admin_disable_user_with_username_attributes tests/test_cognitoidp/test_cognitoidp.py::test_initiate_auth_USER_PASSWORD_AUTH_unconfirmed_user tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_standard_attribute_with_changed_data_type_or_developer_only[standard_attribute] tests/test_cognitoidp/test_cognitoidp.py::test_respond_to_auth_challenge_with_invalid_secret_hash tests/test_cognitoidp/test_cognitoidp.py::test_add_custom_attributes tests/test_cognitoidp/test_cognitoidp.py::test_admin_enable_user tests/test_cognitoidp/test_cognitoidp.py::test_admin_reset_password_disabled_user tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_string_schema_max_length_over_2048[invalid_max_length] tests/test_cognitoidp/test_cognitoidp.py::test_admin_create_user_with_existing_username_attribute_fails tests/test_cognitoidp/test_cognitoidp.py::test_list_users tests/test_cognitoidp/test_cognitoidp.py::test_forgot_password tests/test_cognitoidp/test_cognitoidp.py::test_list_users_inherent_attributes tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_domain_custom_domain_config tests/test_cognitoidp/test_cognitoidp.py::test_sign_up_existing_user tests/test_cognitoidp/test_cognitoidp.py::test_update_group tests/test_cognitoidp/test_cognitoidp.py::test_admin_delete_user_attributes_non_existing_pool tests/test_cognitoidp/test_cognitoidp.py::test_confirm_sign_up tests/test_cognitoidp/test_cognitoidp.py::test_add_custom_attributes_existing_attribute tests/test_cognitoidp/test_cognitoidp.py::test_list_users_returns_limit_items tests/test_cognitoidp/test_cognitoidp.py::test_admin_get_missing_user_with_username_attributes tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_invalid_schema_values[invalid_min_value] tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_client_returns_secret tests/test_cognitoidp/test_cognitoidp.py::test_admin_get_user_with_username_attributes tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool__overwrite_template_messages tests/test_cognitoidp/test_cognitoidp.py::test_list_groups tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_attribute_partial_schema tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_custom_attribute_developer_only tests/test_cognitoidp/test_cognitoidp.py::test_sign_up_with_username_attributes tests/test_cognitoidp/test_cognitoidp.py::test_admin_get_missing_user tests/test_cognitoidp/test_cognitoidp.py::test_setting_mfa_when_token_not_verified tests/test_cognitoidp/test_cognitoidp.py::test_admin_create_existing_user tests/test_cognitoidp/test_cognitoidp.py::test_list_user_pool_clients tests/test_cognitoidp/test_cognitoidp.py::test_list_user_pools_when_max_items_more_than_total_items tests/test_cognitoidp/test_cognitoidp.py::test_forgot_password_nonexistent_client_id tests/test_cognitoidp/test_cognitoidp.py::test_admin_confirm_sign_up_non_existing_pool tests/test_cognitoidp/test_cognitoidp.py::test_authentication_flow_invalid_user_flow tests/test_cognitoidp/test_cognitoidp.py::test_initiate_auth_for_unconfirmed_user tests/test_cognitoidp/test_cognitoidp.py::test_list_users_in_group tests/test_cognitoidp/test_cognitoidp.py::test_list_users_with_username_attributes tests/test_cognitoidp/test_cognitoidp.py::test_authentication_flow_invalid_flow tests/test_cognitoidp/test_cognitoidp.py::test_initiate_auth_USER_PASSWORD_AUTH tests/test_cognitoidp/test_cognitoidp.py::test_update_user_attributes_unknown_accesstoken tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_string_schema_min_bigger_than_max tests/test_cognitoidp/test_cognitoidp.py::test_admin_disable_user tests/test_cognitoidp/test_cognitoidp.py::test_admin_remove_user_from_group_with_username_attributes tests/test_cognitoidp/test_cognitoidp.py::test_admin_update_user_attributes tests/test_cognitoidp/test_cognitoidp.py::test_list_identity_providers_returns_next_tokens tests/test_cognitoidp/test_cognitoidp.py::test_change_password tests/test_cognitoidp/test_cognitoidp.py::test_admin_delete_user_attributes_non_existing_attribute tests/test_cognitoidp/test_cognitoidp.py::test_authentication_flow tests/test_cognitoidp/test_cognitoidp.py::test_admin_user_global_sign_out_twice tests/test_cognitoidp/test_cognitoidp.py::test_admin_remove_user_from_group tests/test_cognitoidp/test_cognitoidp.py::test_admin_confirm_sign_up_non_existing_user tests/test_cognitoidp/test_cognitoidp.py::test_change_password_with_invalid_token_raises_error tests/test_cognitoidp/test_cognitoidp.py::test_describe_user_pool tests/test_cognitoidp/test_cognitoidp.py::test_describe_user_pool_resource_not_found tests/test_cognitoidp/test_cognitoidp.py::test_initiate_auth_REFRESH_TOKEN tests/test_cognitoidp/test_cognitoidp.py::test_admin_setting_mfa tests/test_cognitoidp/test_cognitoidp.py::test_admin_add_user_to_group_again_is_noop tests/test_cognitoidp/test_cognitoidp.py::test_list_users_when_limit_more_than_total_items tests/test_cognitoidp/test_cognitoidp.py::test_admin_resend_invitation_missing_user tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_invalid_schema_values[invalid_max_length] tests/test_cognitoidp/test_cognitoidp.py::test_admin_user_global_sign_out_unknown_userpool tests/test_cognitoidp/test_cognitoidp.py::test_admin_delete_user_attributes tests/test_cognitoidp/test_cognitoidp.py::test_change_password__using_custom_user_agent_header tests/test_cognitoidp/test_cognitoidp.py::test_describe_user_pool_domain tests/test_cognitoidp/test_cognitoidp.py::test_list_user_pools tests/test_cognitoidp/test_cognitoidp.py::test_admin_delete_user_attributes_non_existing_user tests/test_cognitoidp/test_cognitoidp.py::test_update_identity_provider tests/test_cognitoidp/test_cognitoidp.py::test_admin_add_user_to_group tests/test_cognitoidp/test_cognitoidp.py::test_list_users_invalid_attributes tests/test_cognitoidp/test_cognitoidp.py::test_confirm_forgot_password_legacy tests/test_cognitoidp/test_cognitoidp.py::test_delete_group tests/test_cognitoidp/test_cognitoidp.py::test_update_user_pool_client tests/test_cognitoidp/test_cognitoidp.py::test_create_group_with_duplicate_name_raises_error tests/test_cognitoidp/test_cognitoidp.py::test_list_user_pools_returns_max_items tests/test_cognitoidp/test_cognitoidp.py::test_update_identity_provider_no_identity_provider tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_standard_attribute_with_changed_data_type_or_developer_only[developer_only] tests/test_cognitoidp/test_cognitoidp.py::test_initiate_auth_USER_SRP_AUTH_with_username_attributes tests/test_cognitoidp/test_cognitoidp.py::test_admin_reset_password_and_change_password tests/test_cognitoidp/test_cognitoidp.py::test_get_user tests/test_cognitoidp/test_cognitoidp.py::test_confirm_forgot_password_opt_in_verification_invalid_confirmation_code tests/test_cognitoidp/test_cognitoidp.py::test_initiate_auth_USER_SRP_AUTH tests/test_cognitoidp/test_cognitoidp.py::test_setting_mfa tests/test_cognitoidp/test_cognitoidp.py::test_forgot_password_user_with_all_recovery_attributes tests/test_cognitoidp/test_cognitoidp.py::test_initiate_auth_USER_PASSWORD_AUTH_with_FORCE_CHANGE_PASSWORD_status tests/test_cognitoidp/test_cognitoidp.py::test_admin_delete_user_with_username_attributes tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_domain tests/test_cognitoidp/test_cognitoidp.py::test_admin_reset_password_multiple_invocations tests/test_cognitoidp/test_cognitoidp.py::test_list_users_returns_pagination_tokens tests/test_cognitoidp/test_cognitoidp.py::test_resource_server tests/test_cognitoidp/test_cognitoidp.py::test_admin_enable_user_with_username_attributes tests/test_cognitoidp/test_cognitoidp.py::test_list_user_pool_clients_returns_max_items tests/test_cognitoidp/test_cognitoidp.py::test_confirm_forgot_password_with_non_existent_client_id_raises_error tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_custom_attribute_defaults tests/test_cognitoidp/test_cognitoidp.py::test_create_identity_provider tests/test_cognitoidp/test_cognitoidp.py::test_list_identity_providers tests/test_cognitoidp/test_cognitoidp.py::test_initiate_auth_with_invalid_secret_hash tests/test_cognitoidp/test_cognitoidp.py::test_list_user_pool_clients_returns_next_tokens tests/test_cognitoidp/test_cognitoidp.py::test_delete_user_pool_domain tests/test_cognitoidp/test_cognitoidp.py::test_admin_list_groups_for_user_with_username_attribute tests/test_cognitoidp/test_cognitoidp.py::test_admin_list_groups_for_user_ignores_deleted_group tests/test_cognitoidp/test_cognitoidp.py::test_list_users_incorrect_filter tests/test_cognitoidp/test_cognitoidp.py::test_get_group tests/test_cognitoidp/test_cognitoidp.py::test_list_identity_providers_returns_max_items tests/test_cognitoidp/test_cognitoidp.py::test_delete_user_pool_client tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_attribute_with_schema tests/test_cognitoidp/test_cognitoidp.py::test_admin_get_user tests/test_cognitoidp/test_cognitoidp.py::test_update_user_pool_client_returns_secret tests/test_cognitoidp/test_cognitoidp.py::test_confirm_sign_up_with_username_attributes tests/test_cognitoidp/test_cognitoidp.py::test_admin_user_global_sign_out tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_number_schema_min_bigger_than_max tests/test_cognitoidp/test_cognitoidp.py::test_update_identity_provider_no_user_pool tests/test_cognitoidp/test_cognitoidp.py::test_sign_up tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool tests/test_cognitoidp/test_cognitoidp.py::test_admin_resend_invitation_existing_user tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_unknown_attribute_data_type tests/test_cognitoidp/test_cognitoidp.py::test_describe_user_pool_client tests/test_cognitoidp/test_cognitoidp.py::test_update_user_pool_domain tests/test_cognitoidp/test_cognitoidp.py::test_initiate_auth_invalid_auth_flow tests/test_cognitoidp/test_cognitoidp.py::test_global_sign_out_unknown_accesstoken tests/test_cognitoidp/test_cognitoidp.py::test_delete_user_pool tests/test_cognitoidp/test_cognitoidp.py::test_admin_delete_user tests/test_cognitoidp/test_cognitoidp.py::test_initiate_auth_USER_PASSWORD_AUTH_user_not_found tests/test_cognitoidp/test_cognitoidp.py::test_admin_reset_password_unconfirmed_user tests/test_cognitoidp/test_cognitoidp.py::test_initiate_auth_USER_PASSWORD_AUTH_user_incorrect_password tests/test_cognitoidp/test_cognitoidp.py::test_admin_add_user_to_group_with_username_attributes tests/test_cognitoidp/test_cognitoidp.py::test_admin_set_user_password tests/test_cognitoidp/test_cognitoidp.py::test_admin_reset_password_no_verified_notification_channel tests/test_cognitoidp/test_cognitoidp.py::test_set_user_pool_mfa_config tests/test_cognitoidp/test_cognitoidp.py::test_describe_identity_providers tests/test_cognitoidp/test_cognitoidp.py::test_describe_user_pool_estimated_number_of_users tests/test_cognitoidp/test_cognitoidp.py::test_admin_user_global_sign_out_unknown_user tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_custom_attribute_without_data_type tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_client tests/test_cognitoidp/test_cognitoidp.py::test_list_users_in_group_ignores_deleted_user tests/test_cognitoidp/test_cognitoidp.py::test_admin_create_user tests/test_cognitoidp/test_cognitoidp.py::test_delete_identity_providers tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_should_have_all_default_attributes_in_schema tests/test_cognitoidp/test_cognitoidp.py::test_list_user_pool_clients_when_max_items_more_than_total_items tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_invalid_schema_values[invalid_min_length] tests/test_cognitoidp/test_cognitoidp.py::test_update_user_attributes tests/test_cognitoidp/test_cognitoidp.py::test_initiate_auth_invalid_admin_auth_flow tests/test_cognitoidp/test_cognitoidp.py::test_admin_create_user_with_incorrect_username_attribute_type_fails tests/test_cognitoidp/test_cognitoidp.py::test_token_legitimacy tests/test_cognitoidp/test_cognitoidp.py::test_forgot_password_admin_only_recovery tests/test_cognitoidp/test_cognitoidp.py::test_get_user_unconfirmed tests/test_cognitoidp/test_cognitoidp.py::test_confirm_forgot_password_opt_in_verification tests/test_cognitoidp/test_cognitoidp.py::test_list_users_with_attributes_to_get tests/test_cognitoidp/test_cognitoidp.py::test_create_user_pool_string_schema_max_length_over_2048[invalid_min_length] tests/test_cognitoidp/test_cognitoidp.py::test_forgot_password_nonexistent_user_or_user_without_attributes tests/test_cognitoidp/test_cognitoidp.py::test_create_group tests/test_cognitoidp/test_cognitoidp.py::test_admin_setting_mfa_when_token_not_verified