"Kinky Boots," a story by Harvey Fierstein, is based on the 2005 British movie about a real-life shoe factory that struggles until it finds new life in fetish footwear.
"It's so great. I'm done crying a little bit. But I'm still thrilled and a little stunned," said Lauper, who is making her Broadway debut as a musical writer.
Along with "Kinky Boots," also nominated for best musical were "Bring It on," "A Christmas Story" and "Matilda: The Musical," which was second for most nominations with 12.
Hanks was nominated for his role in Nora Ephron's "Lucky Guy" as Mike McAlary, a gutsy New York City newspaper columnist who won a Pulitzer Prize for exposing that a Haitian immigrant had been sodomized by police officers in 1997.
"This makes me both giddy and nervous, and it could not be more special," Hanks said. "Before this began, I thought I knew what it would be like. But you can't imagine what it is. There's the muscle and the brain, but also the spirit and the heart. And it's fun, if fun also incorporates a huge amount of fear."
Some big names snubbed this year were Jessica Chastain, Al Pacino, Alec Baldwin, Katie Holmes, Bette Midler, Sigourney Weaver, Paul Rudd and Scarlett Johansson. Emilia Clarke of HBO's "Game of Thrones" didn't get a nomination for "Breakfast at Tiffany's," but the show came up empty Tuesday.
The Associated Press contributed to this report.