Arterton joined co-host Stephen Mangan to introduce the show and the opening act, from the stage musical of Charlie and the Chocolate Factory.
The first award - for best revival - went to Ghosts at the Almeida Theatre and the Trafalgar Studios.
It was accepted by director Sir Richard Eyre, who joked that the crowds outside the Royal Opera House had mistaken him for nightclub owner Peter Stringfellow, before paying tribute to the "most wonderful cast", which includes Lesley Manville.
Ghosts triumphed again when another member of its cast, Jack Lowden, was named the best actor in a supporting role.
Sir Richard said the awards, which recognise commercial hits as well as subsidised theatres like the National, showed the healthy "ecology" of the theatre.
He said: "For all the successes, you have to be able to fail and that is what subsidy gives you."
Sir Richard beat big names including Mark Gatiss to the prize, before Sharon D Clarke won the best actress in a supporting role award.
The prize for best lighting design was shared between Charlie and the Chocolate Factory and Chimerica - Lucy Kirkwood's play inspired by events in 1989 in Tiananmen Square, China.
The best sound design award was also shared, this time between Chimerica and the musical revival Merrily We Roll Along.
The award for best costume design, presented by Gok Wan and Alexandra Burke, went to Charlie and the Chocolate Factory, while Chimerica won best set design.
The award for best entertainment and family show went to The Wind in the Willows, while Jeeves and Wooster in Perfect Nonsense was named best new comedy.
Mangan gave up hosting duties for a moment to applaud the team behind the show, in which he played the idiotic but good-hearted toff Bertie Wooster.