Mathieu Garon made 23 saves as the Tampa Bay 1, at Tampa Bay Times Forum.
Steven Stamkos and Adam Hall netted goals for the Lightning, who won for the fifth time in seven games.
David Desharnais lit the lamp and Carey Price stopped 20-of-22 shots for Montreal, which dropped its fifth straight contest.
The Lightning opened the scoring at the 8:42 mark of the first period when Martin St. Louis sent a pass from the right point that was tipped towards the net by Teddy Purcell. Stamkos grabbed the loose puck to the left of the net before sweeping across to the right and beating Price to the far side of the net.
But Desharnais sent the game into the first intermission tied at one when he raced down the ice after a Tampa Bay turnover and sent a wrister from the slot into the top-right corner with 3:58 remaining in the opening frame.
Tampa Bay, though, broke the tie just 28 seconds into the second period after Montreal forward Max Pacioretty threw an errant cross-ice pass inside the Lightning's defensive zone.
J.T. Wyman grabbed the loose puck and started up the ice before bouncing a lead pass to Ryan Malone off the boards. Malone then raced to the bottom of the left circle, where he fed a pass to Hall in front of the net and he redirected it home.
The Canadiens were later awarded a five-minute power play in the second period after Malone was given a fighting major and a game misconduct for pummeling on the back of the head of Montreal's Brad Staubitz after the two players collided in the neutral zone. Malone had to be pulled off Staubitz by a referee and then restrained as he tried to run at him again.
Montreal, though, failed to capitalize on the opportunity as Garon made several big saves to keep Tampa Bay on top.
The Canadiens were given another man advantage in the middle stanza and one more in the third period, but they would not be able to tally the equalizer as Garon made nine saves in the second period and six more stops in the third to hold off Montreal.
Purcell had an assist to extend his career-high point streak to seven games. He has four goals and 10 assists in the streak...Staubitz was given an interference penalty and a 10-minute misconduct for his altercation with Malone...Both teams went 0-for-3 on the power play.