Liza Minnelli gave a surprise performance Sunday at the Carlyle Hotel’s Bemelmans Bar on what would’ve been her mother Judy Garland’s 90th birthday. Spies said Minnelli was with Michael Feinstein and “Desperate Housewives” creator Marc Cherry to see Jim Caruso and Billy Stritch at one of their weekly June gigs. “Jim just asked Liza if she wanted to sing,” said a spy, “and the crowd cheered her to do it.” Minnelli suggested she and Feinstein join in a rendition of “I Love a Violin” (originally made popular by Minnelli’s godmother and “Eloise” books author Kay Thompson). “That was the final song of the set,” said our spy, adding, “After all, how could they top it?” Minnelli posted on her Facebook page Sunday of Garland, “Mama gave each and every one of us the gift of hope, laughter and love.” Meanwhile, up on the Carlyle’s 28th floor, Tracie Bennett, who plays Garland in “End of the Rainbow,” was simultaneously celebrating a Tony nomination at O&M Co.’s awards bash. Minnelli — who earlier Sunday was at “The Gershwins’ Porgy and Bess” to wish Audra McDonald and the cast luck — has three Tonys, plus an Oscar, an Emmy and a Grammy. About the only award she hasn’t gotten yet is a Kennedy Center Honor.