The 'Les Miserables' star dressed as Sally Bowles - the character played by Liza Minnelli in the movie - for the performance at Joe's Pub in New York City, and wowed an audience including producer Harvey Weinstein and choreographer Kathleen Marshall.
A source told the New York Post newspaper: "Anne vamped like Audrey Hepburn and sounded like Liza Minnelli. She dressed as Sally Bowles in tiny black satin shorts, black undershirt, a bow tie and boots, with dark, cropped hair and green nail polish."
Also on stage with her was her 'Les Miserables' co-star, British actor Eddie Redmayne.
Eddie - who plays rebel Marius Pontmercy in the film - praised Anne's performance in 'Les Miserables' recently, saying she brought a new feeling to a story that has been told repeatedly.
He said: "When I saw the trailer with Anne singing with this extraordinary fragility, that song I thought I knew pretty well ... suddenly, I listened to the lyrics for the first time, afresh."
Anne recently married partner Adam Shulman in a ceremony in Los Angeles.