How do I setup Drupal/Varnish caching so Content Editors don't see browser-cached pages after logging in?
See the answer to this question:
https://drupal.stackexchange.com/a/117984/3279

Example usage for the D6 varnish module can seen here:
https://www.drupal.org/node/738420

So, you could do a hook_form_alter in a custom php module for D7 that adds an additional submit handler to your nodes that basically calls the D7 equivalent code to clear the varnish caches for the 1 node path path/aliases in question.