It was a critical matchup between teams trying to keep their post-season hopes alive. The Sabres entered the game 10th overall in the Eastern Conference, five points behind the Canadiens.
Montreal's Alexei Kovalev forced the five-minute extra session with his 21st and 22nd goals in the third period. The 22nd created a 3-3 tie at the 15:14 mark.
Tim Connolly (power play, unassisted) had a goal and an assist.
Adam Mair and Clarke MacArthur also scored, while Ryan Miller was credited with 32 saves on 35 shots for the Sabres, who have won two straight after a four-game losing streak.
Christopher Higgins scored once and Carey Price yielded three goals on 37 shots for the Canadiens, who have split their last four games.