With P.K. Subban in the penalty box on a hooking call, the Thrashers went on a 4-on-3 power play and Byfuglien got the game-winner, his team-leading 16th goal of the year, on a slap shot off assists from Tobias Enstrom and Evander Kane.
Ondrej Pavelec withstood a barrage of Canadiens shots, turning aside 47-of-50 attempts to earn the win.
Tomas Plekanec, Subban and Brian Gionta scored for the Habs, and Carey Price made 24 saves as Montreal lost for the fourth time in five contests.
Notable deaths of 2014 [PHOTOS]