Cher kicked off NYC’s Pride Week with a promised live appearance at Marquee — but the icon didn’t show up until 2 a.m. yesterday, and she lip-synced to a few songs.

Despite the late hour, the crowd at the Catwalk party went wild when Cher appeared and introduced her new single, “Woman’s World,” and said, “It’s good to be back in New York, since it was my home for a long time.”

Cher, standing below a giant neon LED signature of her name, told the crowd. “My first gay friend was when I was 9 years old — and I said this on Twitter — but I thought gay was a code word for fun.”

She went on to thank her gay fans, saying, “I have had ups and downs in my career, and you guys have never left me. I was out, I was uncool, I was a has-been, whatever the [bleep].”

She added, “You guys have always been there . . . You’ve kept me in sequins.”

Cher was joined by Andy Cohen — on whose show she had just admitted to having had a lesbian fling in her youth — her rep Liz Rosenberg, as well as DJ Tracy Young (who has worked with the legend as well as Madonna and Britney Spears).

They watched a 15-minute fashion show that included Cher impersonators clad in headdresses, beads and bodysuits. “They lip-synced her songs into mikes as they walked the runway,” says a spy. “Cher was totally digging it.”

Guests at the Susanne Bartsch– and Brandon Voss-hosted event also displayed their most outrageous looks. “It was go-go boys in thongs, girls with their boobs out, people dressed in weird costumes with horns,” said an attendee. “It was like Studio 54 on crack, with Cher mingling with common club kids and freaky partygoers.”

While most were overjoyed to see the “Believe” singer, some were left underwhelmed. “Cher didn’t sing; she just did a little half-hearted dance and left after an hour,” groused a fan.

Perhaps she was just conserving her energy — Cher plays tomorrow’s sold-out Dance on the Pier party.