Mutai clocked two hours four minutes 40 seconds to break the previous mark of 2:05:10 set by compatriot Sammy Wanjiru two years ago. He is now the fourth fastest man in history.
Mary Keitany, the world half-marathon record holder, broke from the field at the halfway stage to win the women's race in 2:19:19.
Keitany, 29, is now equal with German Irina Mikitenko as the fourth fastest woman ever after finishing third in her marathon debut in New York last year.
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The only previous Kenyan double in London was in 2004 when Evans Rutto won the men's race and Margaret Okayo finished first in the women's.
Mutai, 26, was prominent in a tightly bunched leading group tracking the two pacemakers until the 30 kms mark when he made his move.
The race quickly resolved into a battle for the minor placings with three times champion Martin Lel outsprinting fellow-Kenyan Patrick Makau to take second place. Both men were given the same time of 2:05:45.
"My dream has come true," Mutai, who finished second last year, said. "Between 36 and 38 kms it was a little difficult but I just tried to push it and in the end I managed it."
Defending champion Liliya Shobukhova headed the leading group in the first half of the women's race but could not respond when Keitany, who has won six successive half-marathons, made the decisive break.
"I didn't surprise myself," Keitany said. "The weather was very nice and I am very happy to have won the marathon today.
Shobukhova was unable to respond, although her time of 1:20:15 broke the Russian record by 10 seconds and is the fastest by a European since Mikitenko's 2:19:19 in Berlin in 2008.
"I am very happy because I broke the record but obviously disappointed to come in second," she said.
