The pair shared the prize for their respective roles in ‘A Star Is Born’ and ‘The Wife’ during Sunday night’s ceremony.
Gaga said it was an honour to receive the gong alongside Glenn, who she revealed is a good friend of her mother’s.
In her emotional acceptance speech, she said: “So I’m so very happy she won this this evening.”
She also thanked director and co-star Bradley Cooper for being a “magical filmmaker” and a “magical human being”.
She said: “I have never had an experience with a director or an actor like I had with you and I will cherish it forever. You seamlessly were both the love of my life and the man behind the camera.”
Glenn also paid tribute to their fellow nominees; Olivia Colman, Emily Blunt, Toni Collette, Melissa McCarthy and Yalitza Aparicio, saying: “I think I can speak for all of the women in this room: We celebrate each other, and we are proud to be in this room together.”
The pair’s joint award was one of two ties on the evening, with Amy Adams honoured for her role in ‘Sharp Objects’ alongside Patricia Arquette for ‘Escape at Dannemora’ in the category of Best Actress In A Limited Series Or Movie Made For Television.
Lady Gaga also appeared on stage to collect the award for Best Song for ‘A Star Is Born’ track ‘Shallow’.
However, it was a night of mixed emotions for the star, who skipped celebrations to be with her dying horse.
Taking to Instagram after the ceremony, Gaga revealed she was rushing to be with the animal, who starred alongside her in her video for single ‘Joanne’.
She wrote: “She will forever be a part of me. I am so very sad. But I wish for your pain to end, and the gates of heaven to open for you.”
The night also saw Mexican film ‘Roma’ become the big winner, taking home the awards for Best Picture and Best Foreign Language Film.
British success came in the form of an award for Olivia Colman’s turn in ‘The Favourite’, earning her the Best Actress In A Comedy gong, while Ben Whishaw also won Best Supporting Actor In A Limited Series Or Movie Made For Television for ‘A Very English Scandal’.
Check out the full list of winners below...
Best Picture: ‘Roma’
Best Actor: Christian Bale - ‘Vice’
Best Actress - Tie: Glenn Close - ‘The Wife’, Lady Gaga - ‘A Star Is Born’
Best Supporting Actor: Mahershala Ali - ‘Green Book’
Best Supporting Actress: Regina King - ‘If Beale Street Could Talk’
Best Acting Ensemble: ‘The Favourite’
Best Director: Alfonso Cuarón - ‘Roma’
Best Animated Feature: ‘Spider-Man: Into the Spider-Verse’
Best Action Movie: ‘Mission: Impossible - Fallout’
Best Comedy: ‘Crazy Rich Asians’
Best Actor In A Comedy: Christian Bale - ‘Vice’
Best Actress In A Comedy: Olivia Colman - ‘The Favourite’
Best Sci-Fi Or Horror Movie: ‘A Quiet Place’
Best Foreign Language Film: ‘Roma’
Best Song: Shallow - ‘A Star Is Born’ (Warner Bros.)
Best Score: Justin Hurwitz - ‘First Man’ (Universal)
Best Drama Series: ‘The Americans’
Best Actor In A Drama Series: Matthew Rhys - ‘The Americans’
Best Actress In A Drama Series: Sandra Oh - ‘Killing Eve’
Best Supporting Actor In A Drama Series: Noah Emmerich - ‘The Americans’
Best Supporting Actress In A Drama Series: Thandie Newton - ‘Westworld’
Best Comedy Series: ‘The Marvelous Mrs. Maisel’
Best Actor In A Comedy Series: Bill Hader - ‘Barry’
Best Actress In A Comedy Series: Rachel Brosnahan - ‘The Marvelous Mrs. Maisel’
Best Supporting Actor In A Comedy Series: Henry Winkler - ‘Barry’
Best Supporting Actress In A Comedy Series: Alex Borstein - ‘The Marvelous Mrs. Maisel’
Best Limited Series: ‘The Assassination of Gianni Versace: American Crime Story’
Best Movie Made For Television: ‘Jesus Christ Superstar Live in Concert’ (NBC)
Best Actor In A Limited Series Or Movie Made For Television: Darren Criss - ‘The Assassination of Gianni Versace: American Crime Story’
Best Actress In A Limited Series Or Movie Made For Television - Tie: Amy Adams - ‘Sharp Objects’, Patricia Arquette - ‘Escape at Dannemora’
Best Supporting Actor In A Limited Series Or Movie Made For Television: Ben Whishaw - ‘A Very English Scandal’
Best Supporting Actress In A Limited Series Or Movie Made For Television: Patricia Clarkson - ‘Sharp Objects’
Best Animated Series: ‘BoJack Horseman’