Moments later, the show was declared the season's Best Revival of a Musical.
"A year ago, I was hosting the Tonys. This is crazy pants," Harris said as he picked up his trophy. "Playing Hedwig is an absolute joy. It is a role I was terrified of. In taking it on, it has changed me and challenged me and it's exhausting and it is so fun to perform it and I love doing it."
Harris also gave a heartfelt shout-out to his longtime partner David Burtka and their 3 1/2-year-old twins, Harper and Gideon.
"I am so sorry that I haven't been able to spend as much time with you as I wish I could -- given the show," he told his kids. "I promise, as soon as this is done, I'll be able to read books to you and put you to sleep. That's coming up soon."
Although Harris has hosted the Tony Awards shows four times in the past, this is the first time he has earned one of the prestigious prizes himself.
Hedwig got its start off-, off-Broadway in 1998 and has since become a cult favorite. The current production marks its premiere on the Great White Way and Harris' first appearance on Broadway since he starred in the 2004 Tony-winning revival of Assassins. His other Broadway credits include Proof and Cabaret.
Harris' Hedwig co-star Lena Hall scored the Tony for Best Featured Actress in a Musical Sunday night, as well.
2014: The Year in Music [PHOTOS]