Musical of the year "A Gentleman's Guide to Love and Murder," tells the story of a man in Edwardian England who discovers he's ninth in line to a family fortune and sets out to kill the eight ahead of him.
It led the competition with 10 nominations, and won four awards for a musical Sunday, including best book, best director and best costume design.
The 68th annual Tonys, which recognize the best of American theater, saw Harris take home a trophy for his portrayal of an East German transgender singer in the revival of "Hedwig and the Angry Inch."
Harris, himself a four-time Tony host, had been favored to take home best lead actor in a musical for his work donning a platinum-blond wig, miniskirt and outlandish makeup in a role that he said Sunday had "terrified" him.
The forty-year-old actor, singer and producer is best-known for his role as Barney Stinson in the hit television series "How I Met Your Mother."
"Hedwig" also received the Tony for best revival of a musical.
In tears, actress Audra McDonald, 44, made history, accepting an unprecedented sixth Tony, this time for her leading role as Billie Holiday in the play "Lady Day at Emerson's Bar and Grill."
She is the first performer to win six Tonys for acting, and the first person to win in each of the four acting categories -- a Tony grand slam.
And actor Bryan Cranston -- best-known as Walter White from the television series "Breaking Bad" -- won best lead actor in a play for his Broadway debut as former US president Lyndon B. Johnson in "All the Way."
The production also won this year's award for best play.
In a closely-fought battle, the trophy for best lead actress in a musical went to Jessie Mueller, 31, for her performance in "Beautiful -- The Carole King Musical" based on the life of the American singer.
Mueller paid tribute to King -- who was at the awards ceremony -- in her acceptance speech.
Meanwhile, Britain took home several awards with Mark Rylance winning best actor in a featured role in a play for his work in "Twelfth Night" and Sophie Okonedo nabbing the corresponding female award for her performance in "A Raisin in the Sun."
- Evening's top prize -
"Beautiful" was in the running for the top prize snagged by "A Gentleman's Guide to Love and Murder," as was the adaptation of Disney's hit animated film "Aladdin" and "After Midnight," a celebration of the Jazz Age.
The Tonys, which are to American theater what the Oscars are to film, are decided by around 800 voters from within the industry, and are awarded in 26 categories.
The 68th annual award ceremony at New York's Radio City Music Hall was hosted by actor Hugh Jackman, with appearances by stars including Bradley Cooper, Kevin Bacon, Lucy Liu, Clint Eastwood, Ethan Hawke, Gloria Estefan, Tina Fey and Patti LaBelle.
Broadway contributed $12 billion to the New York economy during the 2012-2013 season, according to the Broadway League, and welcomed some 12 million theatergoers.