They did that and more, bringing down the house with their magnetic chemistry during a riveting duet of the Oscar-winning song from "A Star Is Born", which also earned them a standing ovation from the crowd.
Gaga later revealed the encouraging words that her co-star told her in their final rehearsal on Saturday ahead of the big night.
"One of the hardest things in life is to be brave enough to be yourself. I wish to everyone that is going to that celebration to feel a joy inside of them. That’s actually what Bradley said to me yesterday, right before we did our last rehearsal for this performance of 'Shallow,''' she said in a press conference afterward when asked what message she'd send to those attending Australia's Mardi Gras celebration.
"He said, ‘Let’s just drop a little bit of joy.’ And I said, ‘Okay.’ And turns out, joy did a whole lot for me."
In addition to getting an ovation from the Hollywood A-listers in attendance, that joy was also felt by those watching at home.
During the performance, Gaga gazed into Cooper's eyes while she sat at the piano with him on a stool next to her as they sang the emotional lyrics. They eventually sat cheek-to-cheek as they reached the song's crescendo.
The crowd was so moved that the duo got a second ovation when they returned to their seats after their time onstage.
The memorable performance turned out to be a harbinger of things to come as "Shallow" won the Oscar for Best Original Song later in the show. Gaga and co-writers Mark Ronson, Andrew Wyatt and Anthony Rossomando took home the trophy, giving Gaga her first Oscar on a resume that includes nine Grammy awards.
She thanked Cooper, who also wrote and directed "A Star Is Born," in her acceptance speech.
"Bradley, there is not a single person on the planet that could’ve sang this song with me but you,'' she said. "Thank you for believing in us. Thank you so much."