Victory saw the 25-year-old set a new personal best as she added the London title to her win in the Chicago Marathon last year.
Kosgei's compatriot Vivian Cheruiyot was second, in a role reversal from last year when she beat Kosgei to finish first in London.
Ethiopia's Roza Dereje was third.
Kosgei left the rest of the elite women's field behind her with a blistering second half of the race.
Cheruiyot was initially able to stay with her when Kosgei made a break at the 20-mile mark but could not maintain the pace and drifted away some four miles from the finish.
According to statistics compiled by the BBC, Kosgei ran the second half of the race in a time of 66 minutes and 42 seconds -- the fastest for the women's event.
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