Fitzpatrick's TD pass came early in the second quarter and Rian Lindell kicked a pair of field goals for Buffalo (3-10), which held the Browns to only 187 yards of offense and forced three turnovers.
Fitzpatrick went 14-of-23 passing for 142 yards and no interceptions and Fred Jackson rushed 29 times for 112 yards for the Bills.
Jake Delhomme completed 12-of-20 pass attempts for a mere 86 yards and was intercepted once for Cleveland (5-8).
Payton Hillis ran the ball 21 times for 108 yards and made four grabs for 10 yards but lost a pair of fumbles in the loss.
Notable deaths of 2014 [PHOTOS]