Taking to the stage, Lady Gaga said she was honoured to share the award with Glenn.
"My mother and Glenn are good friends, I'm so very happy you won this evening. I am so honoured by this. I went to places in my mind and my heart that I didn't know existed," she added.
Taking to Twitter shortly after the awards Gaga expressed pride over also winning Best Song and Best Actress. She also revealed that she had been informed shortly after the awards that her horse, Arabella was dying.
"I am so honoured and blessed to have won both Best Song and Best Actress. My heart is exploding with pride. But it saddens me to say that just after the show I learned that my dear angel of a horse, Arabella, is dying. She is and was a beautiful horse."
Black Panther was another big winner on the night, winning three awards for Best Production Design, Best Costume and Best Visual Effects.