It won four gongs in total and is favourite to pick up the Best Picture award at the Oscars later this month.
Costume romp The Favourite was the biggest victor at the BAFTAs on Sunday, taking seven awards, but Netflix's black and white film Roma picked up the Best Film prize, as well as Director, at Britain's top movie honors.
Cuaron was also named best director at Sunday night's awards ceremony in London.
It won out against "Lord of the Rings" director Peter Jackson´s "They Shall Not Grow Old" in which silent black-and-white footage from World War I was transformed into a 3D colour movie. "I'm very happy that they're embracing diversity.in a time in which the theatrical experience had become so gentrified", Cuaron said on the red carpet about Netflix. "And what is very needed is a balance between the two economic models - the theatres and the (streaming) platforms, because that's only going to be good for cinema".
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"This is for a lead".
"This isn't for the lead it's for 'a' lead and as far as I'm concerned all three of us are the same and should be the lead and it's weird that we can't do that".
"This is for all three of us. It's got my name on it but we can scratch on some other ones".
Rami Malek was named Best Actor for his performance in the Queen biopic Bohemian Rhapsody and Mahershala Ali won the statuette for his work in the US civil rights-era road movie Green Book.
"Roma" won best film and best director, sharing the glory with British black comedy "The Favourite" which picked up best actress for Olivia Colman as Queen Anne and best supporting actress for Rachel Weisz playing her confidante and lover. Malek, who called his win "truly extraordinary", did express his gratitude to Dexter Fletcher, who stepped in for Singer but is not a credited director on the film. "A Star is Born" won the award for best original music.
Rami Malek won leading actor for "Bohemian Rhapsody", and Mahershala Ali won supporting actor for "Green Book".