The highly anticipated film hits theaters on Oct. 5.
During the panel, Lukas Nelson, who co-wrote many of the movie's songs, tells Gaga, "You just destroyed every single scene you were in."
Gaga immediately tears up, with the crowd erupting in applause for the "Born This Way" singer. While the audience is busy giving her a standing ovation, Gaga -- who opted for a gem-encrusted, silver dress along with a black sparkly hat for the occasion -- sits emotionally, with her lips quivering and eyes moistening.
While the extended applause rings out, Gaga reaches out for 43-year-old Cooper, who immediately grabs her arm to comfort her. Cooper then jumps out of his seat to join in on the standing ovation, which makes Gaga cover her face with her hand before mouthing, "please stop" and "thank you" at the crowd.
The sweet moment ends with Gaga standing in appreciation, blowing the audience a kiss and giving Cooper a hug.
ET recently caught up with the loving co-stars, who couldn't stop singing each other's praises.
"He's so talented. And he's such a visionary and so brilliant, it could just make me cry," Gaga gushed about Cooper. "I just believe in him so much."
In the film, Gaga stars as Ally, an unknown singer-songwriter who is discovered by Cooper's Jackson Maine, a country star.
"The chemistry was instant," Cooper said of his first meeting with Gaga. "[From] the minute that she was kind enough to let me come and talk to her about this potential project. So the fact that we forged a friendship by creating art together is kind of the most idyllic way to use that chemistry."
A Star Is Born hits theaters on Oct. 5. Until then, here's more of ET's sit-down interview with the pair:
Lady Gaga 'Humbled' to Work With 'Visionary' Bradley Cooper in His Directorial Debut (Exclusive)
Lady Gaga Says She 'Very Much Identified With' Both Characters in 'A Star Is Born' (Exclusive)