Gaga, who played upcoming pop star Ally in the movie, was seated at a piano while Cooper, who portrayed ageing rocker Jackson, sat opposite her.
Midway through the song, Cooper moved alongside Gaga and they spent much of the performance staring intensely into each other’s eyes before resting their heads together.
Gaga, who won best original song for the track, has now paid tribute to Cooper, writing on Instagram alongside a picture of the pair: “Nothing could be more special than sharing this moment at the Oscars with a true friend and artistic genius.”
The intense performance led to fans calling for Gaga and Cooper to get together in real life, despite the actor being in a relationship.
Cooper’s girlfriend, the model Irina Shayk, was watching the romantic performance from the front row inside the Dolby Theatre.
It was reported earlier this month that Gaga split with her fiancé, Christian Carino.
Mel B said she felt “uncomfortable” for Shayk – who has a daughter with Cooper – throughout the song.
Speaking on Good Morning Britain, she said: “I felt so uncomfortable for Bradley’s girlfriend, oh my gosh.
“I would like to think it was part of the whole performance because there’s a women’s code and hopefully that’s not… hopefully, it’s only professional.”