"The Book of Mormon" - which stormed London just as it earlier wowed New York - won four prizes, including best new musical and best actor in a musical, for Gavin Creel.
Director Casey Nicholaw said the success of the show - written by "South Park" creators Trey Parker and Matt Stone - came down to its blend of "good contemporary satire and good old-fashioned entertainment."
Lucy Kirkwood's "Chimerica," a play about the entwined fates of China and the United States that opens with a search for the protester photographed standing in front of a tank in Tiananmen Square in 1989, won five trophies including best new play and best director, for Lyndsey Turner.
It was one of several winners to start life in state-subsidized off-West End venues. "Chimerica" opened at north London's 300-seat Almeida Theatre before transferring to a bigger commercial playhouse.
The same path was followed by an acclaimed revival of Henrik Ibsen's "Ghosts," which took prizes for best revival, best actress, for Lesley Manville, and best supporting actor, for Jack Lowden.
"Oh, Larry, where have you been all my life?" said a delighted Manville, clutching her statuette - a bust of acting legend Laurence Olivier.
Director Richard Eyre adapted the play, distilling Ibsen's 19th-century script down to an intense, audience-draining 90-minutes.
"Suicide, euthanasia, feminism, syphilis, morality - you name it, it's in the play," Eyre said, proclaiming Ibsen a "genius."
Lowden - a rising star who will soon be seen in the BBC's television adaptation of Tudor saga "Wolf Hall" - said he was thrilled to win for his performance as the syphilitic son of a troubled family in the intense Norwegian family tragedy.
"Any chance you get to play an arrogant, rash ... drunk, take it," Lowden advised his fellow actors.
Sharon D. Clarke was another winner from the subsidized sector, taking the best-actress trophy for "The Amen Corner" at the National Theatre.
The victories are a boost for state-funded arts groups at a time when Britain's Conservative-led government is cutting all forms of public spending in a bid to reduce the country's huge deficit.
Eyre said subsidized and commercial theater "feed each other."
"You can't have one without the other. ... For all the successes, you have to be able to fail, and that is what subsidy gives you."
Busker romance "Once" won the prize for outstanding achievement in music, and its Croatian co-star, Zrinka Cvitesic, was named best actress in a musical.
"I don't know if you guys are aware of this, but you just changed Croatian history," she said.
The awards, Britain's equivalent of Broadway's Tonys, honor achievements in London theater, musicals, dance and opera.
Founded in 1976, the Oliviers have been laying on the glitz in recent years, with glossy ceremonies modeled on the Tonys.
This year's hosts were actors Gemma Arterton and Stephen Mangan, and performers included tenor Joseph Calleja, Broadway legend Bernadette Peters and ABBA's Benny Andersson and Bjorn Ulvaeus, who reunited onstage to celebrate the 15-year West End run of "Mamma Mia."
Winners in most categories were chosen by a panel of stage professionals and theatergoers. The Audience Award, decided by public vote, went to "Les Miserables."
There were special achievement awards for impresario Michael White - who was behind taboo-breaking shows such as "Oh! Calcutta!" and "The Rocky Horror Show" - and to Hicholas Hytner and Nick Starr, the National Theatre's outgoing management team.
Screen stars Jude Law, Tom Hiddleston and Judi Dench were among the big-name nominees who missed out on acting prizes - Dench to Manville and the men to Rory Kinnear, one of Britain's leading stage actors, awarded for his scheming Iago in "Othello" at the National Theatre.
Kinnear said the fact that in-demand movie actors like Dench, Hiddleston and Law kept returning to the London stage "shows how addictive it is."
"We as actors basically have to do the same job no matter where it is," said Kinnear, who appeared in the James Bond thriller "Skyfall."
"It's using your imagination to fill up people's skin."