"War Horse", based on Michael Morpurgo's children book, took five awards, including best play and best director for a drama, which went to Marianne Elliott and Tom Morris.
First staged in Britain, the spectacular play uses life-size puppet horses to tell the tale of a horse forced to fight on two fronts during World War I.
Other winners included "The Normal Heart," a play about the fight against the AIDS epidemic, which picked up three awards; and a revival of the musical "Anything Goes", first staged in 1934, which also took three awards.
The musical tell the story of two unlikely pairs falling in love aboard a ship, with a crew of singing sailors providing a colorful backdrop.
Norbert Leo Butz won a Tony as best actor in a leading role of a musical: he played the lawman in "Catch Me If You Can," the musical based on the well-known Steven Spielberg movie.
South African playwright Athol Fugard, a leading anti-apartheid campaigner in his country, received a special Tony award for lifetime achievement in the theatre.
"The only way I can make sense of my life is with what I have written on paper," Fugard told reporters. "I consider myself very lucky at this age to continue to have the opportunity to do that."
The Tony Awards, which are given for best Broadway achievement, are considered the theater equivalent of the Oscars.
This year's ceremony was moved from Radio City Music Hall to the smaller Beacon Theatre, which seats only 3,000 people and where Martin Scorsese filmed "Shine a Light," his 2008 documentary about a concert by The Rolling Stones.
The surprises included the lack of any recognition for famed actors Al Pacino and Vanessa Redgrave, who had been nominated for best actor and best actress but left the ceremony empty-handed.
These awards went to Mark Rylance, who starred in "Jerusalem", and Frances McDormand, the lead actress in "Good people."
Attending celebrities included Bono, the lead singer of the Irish band U2, The Edge and actress Brooke Shields.
The Tony Awards were instituted in 1947 by a committee of American Theatre Wing, a New York-based organization dedicated to supporting excellence and education in theatre, and named after Antoinette "Tony" Perry, an actress, director and producer who died in 1946.
The record for the most Tony Awards is still held by "The Producers," which holds 12 coveted prizes.