Renee Zellweger won best actress for playing Judy Garland in Judy. Joaquin Phoenix was named best actor for Joker.
Brad Pitt and Laura Dern scooped the supporting acting awards for their roles in Once Upon A Time in Hollywood and Marriage Story respectively.
Parasite won four awards in total, while Sir Sam Mendes's 1917 took three.
The World War One epic had been the favourite to win best picture, but its awards all came in the technical categories.
Parasite's Bong Joon-ho beat Sir Sam to the prize for best director, and also took the best original screenplay award.
The film is a vicious social satire about two families from different classes in Seoul - one who live in poverty in a semi-basement, and another rich family residing in a large home.
It has now managed what no other subtitled film has done in the 92-year history of the Academy Awards and won best picture.