Tom Francis also won the best actor in a musical gong for his role in the show at the Savoy Theatre.
Sunset Boulevard has earned seven wins following a starring turn from Nicole Scherzinger.
The US actress and singer won the best actress in a musical gong at the Royal Albert Hall as the reinterpretation of the 1950 black comedy of the same name also picked up best director and best musical revival.
Tom Francis also won the best actor in a musical gong for his role in the show at the Savoy Theatre.
Referring to her almost tripping before accepting her award on stage at the Royal Albert Hall, Scherzinger said: “Thank God for saving me from that trip right there,” before adding that she was “nothing without him”.
The Pussycat Dolls singer also said that “coming from really humble beginnings I always wanted to be a singer and do musicals”.
She added that she wanted to do “so many roles” and joked that the failing Hollywood star, Norma Desmond, depicted in the original film, was not “one of them”.
Meanwhile, Dame Arlene Phillips also received a standing ovation following her winning her first competitive Olivier for her choreography on the musical Guys & Dolls.
The 80-year-old former Strictly Come Dancing star thanked fellow choreographer James Cousins for helping her by “crawling around” on the floor to demonstrate the movements when she had issues with her knees.
Succession star Sarah Snook won best actress in a play for her performance in the one-woman show The Picture Of Dorian Gray and Mark Gatiss secured best actor in a play for The Motive And The Cue at the National Theatre.
Gatiss told the audience that the announcer had mispronounced his name, before thanking his husband, actor and writer Ian Hallard, for “putting up with his haircut”.
He beat UK actors Joseph Fiennes, who played England manager Gareth Southgate in Dear England, Happy Valley’s James Norton, Doctor Who star and Scottish actor David Tennant and Irish star Andrew Scott.
Snook paid tribute to Oscar Wilde, the author of The Picture Of Dorian Gray, for coming up with the story in the first place and paid tribute to the one-woman show’s production staff and director.
The Olivier for best new play went to Dear England by James Graham, who thanked the teachers at his Nottingham comprehensive school which he said was in the “red wall”.
He added that he was “so grateful” to his teachers for thinking “working class kids” should learn theatre.
Best actress in a supporting role went to When Winston Went To War With The Wireless star Haydn Gwynne, who died last year at the age of 66, and Will Close scooped a best supporting actor win for Dear England at the National Theatre.
Close thanked footballer Harry Kane, whom he played in the production, and Joseph Fiennes for being a “hero”.
He also paid tribute to his mother, saying: “My mum who passed away with Covid … here’s to all the single mums in council housing.”
The first prize of the evening was given to Vanya, starring Scott, for best revival.
The ceremony was hosted by Ted Lasso star Hannah Waddingham.
