The composer’s win comes 19 years after the last woman, Lisa Gerrard, won in that category for Gladiator – though that was shared with Hans Zimmer.
Speaking after the win, Guðnadóttir admitted she was “speechless” as she scored one of two wins for Joker. Joaquin Phoenix also won Best Performance By An Actor In A Motion Picture – Drama.
Among the other nominees in the Original Score category were Randy Newman (Marriage Story), Alexandre Desplat (Little Women), Thomas Newman (1917) and Daniel Pemberton (Motherless Brooklyn).
The other big musical win of the night was Elton John and Bernie Taupin, who took home Best Original Song for ‘I’m Gonna Love Me Again’ from Rocketman.
Taron Egerton also won Best Actor in a Motion Picture (Comedy or Musical) for playing John in the movie, with the singer himself seen cheering wildly when the actor was announced.
“I’m so honoured to be nominated alongside a bunch of legitimate icons”, he said. “This role has changed my life. It’s been the best experience of my life.”
Paying tribute to the man he portrayed, Egerton added: “To Elton John, thank you for the music, thank you for living life less ordinary, and thank you for being my friend.”
The big winner of the night was Sam Mendes’ war movie 1917, which won Best Motion Picture (Drama) and Best Director.
On the TV side of things, Phoebe Waller-Bridge’s Fleabag and historical drama Chernobyl were the night’s big winners.