The A Star is Born actress immediately burst into tears when the award was announced by Idris Elba and Taylor Swift, and she continued to cry as co-writer Mark Ronson praised her.
"As a woman in music, it is really hard to be taken seriously as a musician and a songwriter .... they lifted me up, they supported me," Gaga also said about her co-writers, which include Anthony Rossomando and Andrew Wyatt.
I am so beyond grateful for this Golden Globe & honored to have won it w/ @MarkRonson@Wyattish , Anthony Rossomando and to have sang it with Bradley Cooper. I also could not be happier for Glenn Close winning tonight. She is a true legend and deserves every award. Thank you HFPA pic.twitter.com/Dpw2QNmFD3
A Star is Born is up for five major awards at this year's Golden Globes, including Best Motion Picture - Drama, Best Actress for Gaga, Best Actor for co-star Bradley Cooper and Best Director for Cooper.
ET spoke to Cooper at the Palm Springs International Film Festival last Thursday, where he marveled at the film's incredible success.
"I was just hoping that I wouldn't fail miserably," he said. "It's vulnerable, you know, writing, co-writing, telling a story and directing it. I mean I had no idea what was going to happen. I just knew that I had to try. So, the fact that it has been well received, I just wanna savor it."
And it's no secret the co-stars have gotten close since filming the tear-jerking drama. ET spoke to 32-year-old Gaga at the gala honoring Cooper as a 32nd American Cinematheque Award honoree last November, where she praised their lasting friendship.
"I just love him so much and he is such a dear friend of mine and I am just so proud to be here tonight," Gaga said, sharing that they've managed to remain friends even after the production wrapped and the promotion cycle came to an end.
"We talk all the time, yeah," she continued. "...You know, that's what's really come out of all of this for me: the reward of a lifetime friendship with someone I deeply respect."
As for Cooper, he told ET last week that despite being in the middle of a busy awards season, he was definitely planning to attend Gaga's Las Vegas residency, Enigma, at Park MGM's Park Theater.
"I can't wait!" he exclaimed. "I wanted to see the opening show and I couldn't make it. I was so bummed. I'm gonna see it soon."