Seated in the front row of Los Angeles' Dolby Theatre, Cooper, 44, and Gaga, 32, entered the stage with no fanfare and no outfit changes, wearing the same tux and black gown that they'd sported on the red carpet.
At the end of Cooper's first verse, Gaga sat across from him at the piano, never breaking her intense eye contact with her co-star and director.
W Magazine wrote, "Cooper and Gaga's connection was so strong, at the end of their performance their mouths were a couple of breaths away from a kiss."
The pair received a standing ovation from the crowd and hugged before exiting the stage.
On Jan. 27, Cooper joined Gaga at her Las Vegas Enigma residency to perform "Shallow," which won the Oscar for best original song.
"A Star Is Born" was also up for best picture and best original score.
Cooper and Gaga were nominated for best actor and actress, respectively, but Cooper admitted he was hurt at being snubbed for best director for the film, which was his directorial debut.