The singer, who received a standing ovation after performing the track alongside Bradley Cooper, graced the stage with co-writer, Mark Ronson.
During the acceptance speech, she said: "If you're are at home and you're sitting on your couch, all I have to say is that this is hard work. I've worked hard for a long time and it's not about winning but what's it's about is not giving up. if you have a dream, fight for it."
She continued: "There's a discipline of our passion and it's not about how many times you get rejected, it's about how many times you stand up and are brave and you keep on going."
Earlier in the evening, Black Panther's Hannah Beachler became the first black winner of the Best Production Design award, delivering an emotional speech that was praised by Angela Bassett and Reese Witherspoon.
Winners at this year's ceremony included Olivia Colman for The Favourite, Rami Malek for Bohemian Rhapsody, Regina King for If Beale Street Could Talk and Mahershala Ali whose film Green Book won Best Picture. Alfonso Cuarón took home Best Director for his Netflix drama Roma.
You can find a full list of winners here.
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