Mirren was honoured for her performance as Queen Elizabeth II in Peter Morgan's play The Audience, having won an Oscar for the same role in Morgan's 2006 film The Queen.
Kinnear and Lester were jointly awarded Best Actor for Othello at the National Theatre, beating Chiwetel Ejiofor, who was the only other nominee in their category (for Seasons in the Congo).
And former National Theatre artistic director Richard Eyre overcame competition from current artistic director Nicholas Hytner and AD-in-waiting Rufus Norris to pick up Best Director for his revival of Ibsen's Ghosts at the Almeida, which has just announced a West End transfer.
View our gallery of winners and guests
In the musicals categories, Maria Friedman's Menier Chocolate Factory revival of Sondheim's Merrily We Roll Along won Best Musical, beating The Book of Mormon (which was named Best Night Out on Friday); while Rosalie Craig was awarded the newly created Best Musical Performance award.
Craig, who won for playing the title role in Tori Amos musical The Light Princess at the National, was up against Cynthia Erivo (The Color Purple) and Charlotte Wakefield (The Sound of Music).
A number of Special Awards were also presented on the night - six in total.
David Walliams took home the new 'Award for Comedy' for his performance as Bottom in Michael Grandage's production of A Midsummer Night's Dream. He collected the gong from Dame Edna Everage, whose farewell show has just opened at the Palladium.
Kevin Spacey, artistic director of the Old Vic since 2003, was given the Editor's Award for his contribution to British Theatre.
All told there were 15 awards handed out, including the nine main shortlist categories.
Evening Standard owner Evgeney Lebedev, a noted theatre enthusiast, was on hand to host the evening, while guests at the Savoy included actors Jude Law, Tom Hiddleston, Miranda Hart, Kristin Scott Thomas and Hugh Grant, and politicians Nick Clegg and Boris Johnson.
Sarah Sands, editor of the Evening Standard, said: "The high level of theatrical daring and creativity seen on the London stage this year made our choices tougher than ever to make. We, like the rest of the world, have been dazzled by the talent on show."
To catch up with our Live Tweeting from the ceremony, including speech highlights, click here
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Evening Standard Award winners:
Rory Kinnear & Adrian Lester for Othello (NT Olivier)
Natasha Richardson Award for Best Actress
Helen Mirren for The Audience (Gielgud)
Chimerica by Lucy Kirkwood (Almeida & Harold Pinter)
Ned Sherrin Award for Best Musical
Merrily We Roll Along (Menier Chocolate Factory & Harold Pinter)
Richard Eyre for Ghosts (Almeida)
Bob Crowley for People (NT Lyttelton) & The Audience (Gielgud) & Once (Phoenix)
Charles Wintour Award for Most Promising Playwright
Rachel De-lahay for Routes (Royal Court)
Milton Shulman Award for Outstanding Newcomer
Seth Numrich for Sweet Bird of Youth (Old Vic)
Best Musical Performance
Rosalie Craig for The Light Princess (NT Lyttelton)
Emerging Talent Award (in partnership with Burberry)
Cush Jumbo for Josephine and I, Bush
Award for Comedy
David Walliams for his performance as Bottom in A Midsummer Night's Dream
Beyond Theatre Award
BBC Proms 2013
Kevin Spacey for his contribution to British theatre
Lebedev Special Award
Lord Lloyd-Webber for his contribution to musical theatre
Theatre Icon Award
Dame Maggie Smith for her contribution to the world stage