Bradley was in the audience for Gaga's Enigma show when he appeared on stage to surprises fans for the acoustic performance.
A Star Is Born tells the tragic love story of ME, played by Cooper, who helps Gaga's struggling artist Ally.
He then shared another video from the night, which had fans screaming as Gaga knelt beside Cooper during his part of the song. "Yo Bradley, you wanna come up and do this one?"
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.
After sharing a hug, Gaga announced to Cooper, "I even got you in-ears".
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Consequently I'm not ball-striking at my best. "You've got to keep it going". He continued: "Shoot, I'm still leading, obviously, it's fantastic".
Though he added, "I can't hear anything", Cooper seemed unfazed as he launched into a rendition of the song, which is nominated for an Oscar. He looked into Gaga's eyes as he sang the lyrics that she wrote for the film.
After their performance, Gaga's backup dancers took their bows, with Cooper joining them.