The actor, who also won for Moonlight in 2017, has become the first black man to win the best supporting actor award more than once.
Roma became Mexico’s first winner for best foreign language film, while Cuarón also picked up the award for best cinematography.
The Marvel film also won best original score for composer Ludwig Göransson, a longtime collaborator of director Ryan Coogler.
Green Book has been named best picture in a surprise victory over Roma, during an Oscars ceremony filled with diversity, historic wins and a lack of a host.