Byrne won for her performance as a psychotherapist in If I Had Legs I'd Kick You.
Byrne joins Timothée Chalamet, who was named best male actor in a musical or comedy for his role in Marty Supreme.
Earlier, the 83rd Golden Globes got under way with a pointedly political opening from host Nikki Glaser and an early award for the night's favourite, One Battle After Another.
Glaser, hosting the show for the second straight year, kicked off the Beverly Hills, California, event on a note of self-aware satire.
"Yes, the Golden Globes, without a doubt the most important thing happening in the world right now," Glaser said.
The comedian landed some punch lines on the usual subjects - the age of Leonardo DiCaprio's dates, Kevin Hart's height - before referencing the Epstein files, suggesting best editing should go to the Justice Department.
The night's first award went to Teyana Taylor for her explosive supporting performance in One Battle After Another.
A teary-eyed Taylor took the stage and accepted what could be the first of many awards for Paul Thomas Anderson's film.
"To my brown sisters and little brown girls watching tonight, our softness is not a liability. Our depth is not too much. Our light does not need permission to shine," she said.
Best supporting actor went to Stellan Skarsgård for the Norwegian family drama Sentimental Value, defeating Australia's Jacob Elordi who was nominated for his role in Frankenstein.
It was the first major Hollywood movie award for the 74-year-old, a respected veteran actor who drew a standing ovation.
"I was not prepared for this because I, of course, thought I was too old," said Skarsgård.
Amy Poehler won the inaugural award for podcasting, while KPop Demon Hunters triumphed in the best song category.
One Battle After Another has a leading nine nominations, competing in the Globes' musical or comedy category.
The most comically poignant award of the night went to Seth Rogen, whose Hollywood satire The Studio memorably included an episode devoted to drama around a night at the Globes. (Sample line: "I remember when the red carpet of the Golden Globes actually stood for something.")
Rogen won best male actor in a comedy.
"This is so weird," Rogen said, chuckling. "We just pretended to do this. And now it's happening."
28°C