Cheigat, 27, won the 26-mile-385-yard race in 2 hours 10 minutes 37 seconds ahead of fellow Kenyan Robert Cheboror who finished second in 2:11:49. Cheigat's winning time was the slowest since 1991. Martin Lel of Kenya was third in 2:13:38.
Ndereba, 32, fought through leg cramps in posting her winning time of 2:14:27 and collapsed at the finish line.
Patriots' Day temperatures soared into the mid-80s but the unseasonal heat did not stop the Kenyans who won for the 13th time in 14 years in the men's race and fourth time in five years in the women's.
"It was very hard in that heat," said Cherigat, the training partner of Sunday's London Marathon winner Evans Rutto.
Defending Boston champion Robert Kipkoech Cheruiyot and 2002 winner Rodgers Rop both dropped out of the race.