The winning kick snapped Buffalo's 15-game losing streak to the Pats.
The Bills (3-0) picked off New England's Tom Brady four times in overcoming a 21-0 deficit and notched their first victory over the Patriots since 2003.
Ryan Fitzpatrick went 27-of-40 through the air for 369 yards, two touchdowns and two interceptions while Drayton Florence returned an interception 27 yards for a score in the fourth quarter for the Bills.
Stevie Johnson hauled down eight passes for 94 yards and a score while Donald Jones made five grabs for 101 yards.
Brady finished 30-of-45 passing for 387 yards and four TDs but also yielded four costly interceptions.
Wes Welker made 16 catches for 217 yards and a pair of scores. Rob Gronkowski added seven grabs for 109 yards and two TDs for the New England (2-1).