The actor, who directed and starred in the film which has been nominated for eight Academy Awards, sang the first half of the song while Gaga knelt at his feet.
Lady Gaga performs during her "Enigma" Las Vegas residency in a head-to-toe glittering look, January 26. I don't know if you know him but his name is Bradley.
"I even got you in-ears", Gaga told Cooper after the two embraced, describing the earphone-like monitors used onstage.More news: Osaka comes through Kvitova epic to seal Australian Open glory
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Gaga's show has become a headline-grabber before - just last week, the singer slammed President Trump midway through her 2016 hit "Million Reasons" for the continued government shutdown. The song also received a nomination for best original song.
In video clips shared on social media from concert-goers, Gaga sits at the piano while Cooper is on a stool as they sing the Oscar-nominated track together.
A Star Is Born has opened up a new career path in acting for the singer, who won the Best Actress gong at the recent Critics' Choice Awards.