The Ghostbusters star crashed Letterman's monologue and explained he was there to work on his "bucket list".
Towards the end of the show, Murray expressed his desire to meet Lady Gaga and the singer appeared onstage to a standing ovation from the audience.
After posing for photographs together, Gaga, Murray and Letterman invited fans across the street to the Roseland Ballroom, where she performed the fourth of seven shows on Wednesday. The legendary venue will close for good on 7 April (14).
The Born This Way hitmaker closed the Late Show with David Letterman by performing her songs Dope and G.U.Y.