Hanie, the Bears' back-up signal-caller, capped a nine-play, 47-yard drive with his rushing score for the game's only touchdown.
Marion Barber marked his Chicago debut by piling up 37 on six carries during the scoring drive, finishing the game with 45 yards on seven carries.
Jay Cutler played one series for the Bears, completing the only pass he attempted for no gain.
Buffalo quarterback Ryan Fitzpatrick completed 7-of-9 passes for 44 yards.
Notable deaths of 2014 [PHOTOS]