The Oscar-winning director and his team were presented with the Beyond Theatre award by Team GB's cycling champion Victoria Pendleton.
Judges praised the London 2012 curtain-raiser for its "outstanding work" in taking theatre outside of the traditional stage.
In a star-studded event in central London, National Theatre director Nicholas Hytner walked away with two awards, while playwright Nick Payne became the youngest ever winner in the Best Play category.
The 29-year-old actor was presented with the prestigious prize for his metaphysical love story 'Constellations', starring Sally Hawkins and Rafe Spall.
Sir Nicholas won Best Director for the play 'Timon of Athens' as well as picking up the Lebedev Special Award to mark his decade at the helm of the National Theatre. The 56-year-old's stage successes have included worldwide hits 'War Horse', 'One Man', 'Two Guvnors' and 'The History Boys'.
Dame Judi Dench was honoured for her contribution to world theatre with the Moscow Art Theatre's Golden Seagull award.
Meanwhile, Oscar-winner Cate Blanchett lost out in the Best Actress category to Hattie Morahan who won for her moving interpretation of trapped housewife, Nora, in 'A Doll's House' at the Young Vic theatre.
Simon Russell Beale won Best Actor for his portrayal of Stalin in 'Collaborators', the black comic drama at the National's Cottesloe.
Best Musical went to 'Sweeney Todd', directed by Jonathan Kent and starring Michael Ball and Imelda Staunton.
The awards ceremony was presented by James Corden and attracted a host of stars from theatre, film and music.
