Regulation ended in a 3-3 tie after Montreal's Sergei Kostitsyn (power play) scored his sixth goal this season at 15:06 of the third period.
Kostitsyn scored twice, Alex Tanguay once, Andrei Markov had two assists, and Jaroslav Halak surrendered three goals on 34 shots in the Canadiens' second straight victory following a three-game losing streak.
Buffalo had taken a 2-1 second period lead on goals by Derek Roy in the first and Clarke MacArthur in the second. Andrej Sekera (power play) also scored once.
Teppo Numminen had two assists and Ryan Miller was beaten four times on 46 shots for the Sabres, who had their three-game road winning streak snapped.
On the power play, Montreal was 2-for-7, and Buffalo went 1-for-3.
Swim Week Miami Beach 2014 [PHOTOS]