Fourth in London earlier this year, Biwott won in an unofficial time of two hours, 10 minutes and 34 seconds.
"It was fantastic," said the 29-year-old former dairy farmer. "The pace was slow (in the first half of the race) but I knew that last 15 kilometres I pushed hard."
Kamworor came home in 2:10:48 with Ethiopia's Lelisa Desisa third in 2:12:10.
Defending champion Wilson Kipsang of Kenya faded to fourth.
Former Boston Marathon champion 40-year-old Meb Keflezighi was the top American finisher placing seventh.
Biwott became the 11th different Kenyan to win the New York race. The 2012 Paris marathon champion was second in London in 2014 and fifth in his previous New York marathon in 2013
Keitany surged to the front for keeps shortly after 18 miles and triumphed in an unofficial clocking of 2:24:25.
The tiny Kenyan quickly broke London Marathon champion Tigist Tufa of Ethiopia in the 22nd mile and ran the remainder of the race alone.
She became the first back-to-back New York champion since Briton Paula Radcliffe won in 2007 and 2008.
Despite the high quality field the pace was slow until the soft-spoken Kenyan decided to push the pace.
"When I took my lead, I said, let me just go," said the 33-year-old Keitany. "If someone is enough strong they can come.
There was no incentive for a fast start, she said. "So I had to wait until around 30 km."
Ethiopia's Aselefech Mergia took second in 2:25:32 with compatriot Tufa third.
Laura Thweatt, making her marathon debut, finished seventh as the top American.
Most top U.S. marathoners, both men and women, skipped the race as they prepared for the U.S. Olympic marathon trials in Los Angeles in February.
Russian-born American Tatyana McFadden destroyed the women's wheelchair course record by seven minutes, winning in an unofficial 1:43:04 for her 12th consecutive major marathon victory and third straight in New York.
South African Ernst van Dyk, twice a runner-up, claimed the men's wheelchair race in an unofficial 1:30.54 to edge American Josh George.
(Reporting by Gene Cherry in Salvo, North Carolina. Editing by Steve Keating.)
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