Walker said the play had, through some "magic," succeeded in creating an onstage world as seen through the eyes of a teenage hero with autism.
"You start out thinking (it) is completely different to our world, and you end up thinking 'No, there are parts of this world I understand.'"
The Olivier awards honor achievements in London plays, musicals, dance and opera. Winners in most categories are chosen by a panel of stage professionals and theatergoers.
Founded in 1976, the Oliviers have been laying on the glitz in recent years, with glossy ceremonies modeled on Broadway's Tony Awards.
"Downton Abbey" actor Hugh Bonneville and West End star Sheridan Smith — an Olivier winner in 2011 and 2012 — hosted a sparky ceremony that included performances by "Glee" star Matthew Morrison, Tony-winning "Wicked" diva Idina Menzel and 60s songstress Petula Clark.
The best new musical category had a retro feel, with the trophy going to "Top Hat" — a tap-dancing, tail-coated homage to Hollywood's Golden Age based on the 1935 Fred Astaire-Ginger Rogers movie. It also won awards for costume design and choreography.
Blood-soaked musical "Sweeney Todd" took the prize for best musical revival, with its stars Imelda Staunton and Michael Ball named best actress and actor in a musical.
"I'm not sure I deserve this," Ball said. "But I've also got sciatica, and I don't deserve that either."
Royal Ballet principal dancer Marianela Nunez took the prize for outstanding achievement in dance, while the same company's "Aeternum" was named best new dance production.
An immersive staging of the Philip Glass opera "Einstein on the Beach" at London's Barbican Centre was named best new opera production. American tenor Bryan Hymel won the outstanding achievement in opera prize for performances at the Royal Opera House.
Special achievement awards went to choreographer Gillian Lynne — best known for her work on Andrew Lloyd Webber musicals including "Cats" and "The Phantom of the Opera" — and playwright Michael Frayn, whose classic backstage farce "Noises Off" is still going strong 30 years after its debut.
Jill Lawless can be reached at http://Twitter.com/JillLawless