With the win, the Lightning secured a spot in the playoffs for the first time in three seasons, and moved into the second spot in the Atlantic Division with 93 points. Montreal also has 93 points, but Tampa has a game in hand.
Ryan Callahan and Alex Killorn also scored while Ben Bishop made 25 stops for the Lightning, who have won three of their last four.
Brendan Gallagher had the only goal of the game for the Canadiens, who had a five-game winning streak stopped. Carey Price allowed two goals on 32 shots.