David Letterman -- Marines Get Ship-Faced at After-Party! (VIDEO)

David Letterman had scores of big celebrities at his finale after-party, but the most entertaining guys in the building were 2 Marines who enjoyed a lot of free vodka on Dave.

The 2 guys are in NYC for Fleet Week, and their first night got awesome when they bumped into Steve Martin's wife, who invited them into the shindig.

They told us about all the famous people they met, but it sounds like their new best friend is the bartender.

Happy Memorial Day!!! It's gonna be an awesome Fleet Week.