A mustached Alec Baldwin playing Twain said he thought he would be remembered for being a tender lover and was surprised to learn the prize honors top comics.
"Tina, well that's a funny name for a man," he said, shocked to hear it was a woman who had won because "their brains aren't shaped right."
A hundred years after the author's death, the woman famous for her Emmy Award-winning impression of Sarah Palin on "Saturday Night Live," accepted the Mark Twain Prize for American Humor – even though she feels her style is "so typically Austrian."
She thanked Palin for her success and said she has it on good authority that Sen. John McCain has a picture of Fey in his office and had been getting ideas long before he picked the former Alaska governor as his running mate.
"I guess what I'm saying is, this whole thing might be my fault," she said.
She also thanked the Kennedy Center, which she said will soon be known as "the tea party bowling alley and rifle range."
"SNL" comics lined up to celebrate their colleague's work over nine seasons. They played clips from her time anchoring "Weekend Update" and some of the commercials she wrote, including a spoof on "mom jeans."
"Our dreams were as big as our unshaped eyebrows," Poehler said.
The humor prize honors those who define contemporary comedy. Last year, it went to Bill Cosby. Organizers said Fey made her mark as the first female head writer on "SNL," not to mention her Palin impression and creating the NBC comedy series "30 Rock," in which she stars with Baldwin.
Tracy Morgan acted unimpressed - especially that Fey was the first woman to lead the writing team.
"I was the first male cast member who tried to force an unwanted kiss on the first female head writer," he said.
Earlier, when the prize was announced, Fey hinted she didn't feel worthy, joking that she assumed Betty White was disqualified "for steroid use."
Not to be outdone, on the red carpet, the 88-year-old White praised Fey's "intelligence and her sense of comedy." Then she deadpanned, "Too bad she's not good looking."
White also took the stage to honor Fey. They also performed together on "SNL" in May for which White won rave reviews as host.
Steve Martin, who also has taken home the award, said Fey's win means he's been demoted. He said he loves Fey's parody of Palin, but even more, he said he loves to read her writing.
"Isn't it refreshing to find a comedian who is both really good and funny looking?" he said.
On the big screen, Fey recently starred with Steve Carell in "Date Night" and is a featured voice in "Megamind," which debuted at No. 1 at last weekend's box office. Now she is working on her first book, a memoir due out next year. She lives in New York with her husband, Jeff Richmond, and their daughter.
"SNL's" Fred Armisen said one of his favorite things about Fey is her take on the world.
"She makes fun of people really well - under her breath. It's so funny, so sharp."
The show will be broadcast nationally Sunday on PBS. Kennedy Center Chairman David Rubenstein said the event raised record $1.3 million for center with high demand for tickets – especially from Alaska.