Quickest Method To Invalidate Statistics
The most reliable sequence I can find to cause an automatic statistics update is:


Update statistics sampling zero rows
This results in an empty statistic object.

-- Example
UPDATE STATISTICS 
    Person.[Address] 
    IX_Address_StateProvinceID 
    WITH SAMPLE 0 ROWS;

Update the target column(s) in a single row of the table
This increments the column modification counter. The combination of an empty statistics object and an incremented modification counter enables a special case statistics update (it simulates creating statistics on an empty table, then adding a row).

-- Example
BEGIN TRANSACTION;
    UPDATE TOP (1) 
        Person.[Address] 
    SET StateProvinceID = StateProvinceID;
ROLLBACK TRANSACTION;

Run the query with OPTION (RECOMPILE)
This causes an automatic update of detected stale statistics, even if a matching plan for the query is already present in cache. The resulting statistics update will subsequently cause an optimality-based recompilation for the original cached plan, if it is matched again.

-- Example
SELECT
    A.City,
    A.AddressLine1,
    A.AddressLine2
FROM Person.[Address] AS A
WHERE
    1 = 1
    AND A.StateProvinceID = 54
OPTION (RECOMPILE);



Demo

Using a similar AdventureWorks query as used in jyao's answer, the following script puts everything above together:

DBCC FREEPROCCACHE;
GO
-- Cache a plan for the query
GO
SELECT
    A.City,
    A.AddressLine1,
    A.AddressLine2
FROM Person.[Address] AS A
WHERE
    1 = 1
    AND A.StateProvinceID = 54;
GO
DBCC SHOW_STATISTICS 
(
    'Person.Address', 
    'IX_Address_StateProvinceID'
) WITH STAT_HEADER;
GO
-- Empty stats object
UPDATE STATISTICS 
    Person.[Address] 
    IX_Address_StateProvinceID 
    WITH SAMPLE 0 ROWS;
GO
-- Perform and rollback a single row update
BEGIN TRANSACTION;
    UPDATE TOP (1) 
        Person.[Address] 
    SET StateProvinceID = StateProvinceID;
ROLLBACK TRANSACTION;
GO
DBCC SHOW_STATISTICS 
(
    'Person.Address', 
    'IX_Address_StateProvinceID'
) WITH STAT_HEADER;
GO
-- Run the query again to trigger stats update
GO
SELECT
    A.City,
    A.AddressLine1,
    A.AddressLine2
FROM Person.[Address] AS A
WHERE
    1 = 1
    AND A.StateProvinceID = 54
OPTION (RECOMPILE);
GO
DBCC SHOW_STATISTICS 
(
    'Person.Address', 
    'IX_Address_StateProvinceID'
) WITH STAT_HEADER;
GO


Output

The DBCC SHOW_STATISTICS results show the original statistics header, the empty header, and the desired updated header at the end of the process: