The Favourite won seven trophies, including best British film and best actress for Olivia Colman, who plays Britain's 18th century Queen Anne in the female-centric drama.
Alfonso Cuaron's Roma, which centres on the nanny to a middle-class Mexico City family, took out the prizes for best picture, director, cinematography and foreign-language film.
Cuaron thanked Netflix for backing "a black-and-white film about a domestic worker'' that is not in English.