The winning kick came after Steven Jackson forged a 31-31 tie on a 1-yard scoring run with 1:28 left in regulation following an 11-play, 65-yard drive.
Jackson finished with two scores on 23 carries, rushing for 84 yards, and Matt Ryan made good on 28-for-47 passes for 311 yards and a touchdown as the Falcons (3-9) snapped a five-game losing streak.
The Bills (4-8), meanwhile, fell out of the AFC wild card race with a fourth loss in five contests.
They were led by C.J. Spiller, who rambled for 149 yards on 15 carries with a score.
E.J. Manuel went 18-for-32 passing for 210 yards, supplying a passing and a rushing touchdown for Buffalo.
Notable deaths of 2014 [PHOTOS]