The West End production took home Best New Musical, Best Director (Matthew Warchus), Best Actor in a Musical (Bertie Carvel), and Best Actress in a Musical, presented jointly to the four child stars who share the title role.
Eleanor Worthington-Cox, who at 10 years old became the youngest Olivier Award winner, said of her win, "That's pretty cool. Scary. But I find that pretty amazing."
Matilda also swept the technical categories for choreography, set design and sound design.
The trophy for Mastercard Best Play went to John Hodge's Collaborators, and taking home the prize for Best Actor were Benedict Cumberbatch and Jonny Lee Miller, who alternated the roles of scientist and creature in Danny Boyle's Frankenstein.
Ruth Wilson saw off competition from the likes of Kristen Scott Thomas and Celia Imrie to land Best Actress for her performance in Anna Christie.
The cast of Les Miserables was handed the BBC Radio 2 Audience Award, while Anna Christie was named Best Revival and Crazy for You was the Best Musical Revival.
The Olivier Awards, which celebrate the best of the year's British stage shows, was hosted by Sweeney Todd co-stars Imelda Staunton and Michael Ball at London's Royal Opera House.
Matilda The Musical's big evening eclipsed the previous record set in 1980 by Nicholas Nickleby when it brought home six trophies.