In the middle of her Enigma residency show at the Park MGM on Saturday, the pop icon addressed the crowd: "So a really good friend of mine..."
The actor turned singer and singer turned actor hugged before Lady Gage gave Cooper a pair of "in-ears" and a microphone.
They captured hearts as Jackson and Ally Maine in their film A Star Is Born.
Videos of the performance posted on social media show Cooper sitting on a stool to begin the song, with Gaga squatting next to him, looking up to him and nodding in encouragement as he sang.
While Cooper sang, Gaga knelt beside him and put her arms on his leg.
The crowd reportedly cheered as Cooper made his way to the stage.
The song, which was nominated for an Academy Award earlier this week, is the closing number of the "Enigma" show, the residency that kicked off in December previous year.
The song earned the singer, born Stefani Germanotta, an Academy Award nomination and a Golden Globe Award for best original song.