The Kennedy Center for the Performing Arts awarded Burnett the nation's top humor prize.
Tina Fey opened the show.
"You mean so much to me," Fey said, "I love you in a way that is just shy of creepy."
Julie Andrews, Tony Bennett, Amy Poehler and others performed in the longtime performer's honor.
In an interview on the red carpet Sunday, Burnett said a couple's good deed allowed her to chase her dream to New York.
"A gentleman and his wife lent me the money," said Burnett.
Burnett made a special request that rising comedienne Rosemary Watson, who does impressions of Hillary Clinton and others, be part of the show. Burnett found Watson on YouTube after receiving a fan letter and thought she was funny.
"The thing is, you pay it forward," Burnett said, "because when I got started, somebody gave me a break when I was 21 years old, and I wanted to go to New York."
When Burnett launched her namesake variety show in the 1960s, one TV executive told her the genre was "a man's game." She proved him wrong with an 11-year run that averaged 30 million viewers each week.
The show ran from 1967 to 1978 and included guest stars such as Lucille Ball, Jimmy Stewart, Ronald Reagan and Betty White.
"This is very encouraging," Burnett, 80, deadpanned in accepting the prize. "I mean it was a long time in coming, but I understand because there are so many people funnier than I am, especially here in Washington.
"With any luck, they'll soon get voted out, and I'll still have the Mark Twain prize."
The show was taped Sunday and will be broadcast Nov. 24 on PBS stations.
The Associated Press contributed to this report.