Until Alex Killorn's empty-netter, it looked like the fourth 2-1 game of the season between these teams.
But if it weren't for Carey Price's brilliance, Tampa Bay would have won 6-1.
Brendan Gallagher opened the scoring with his 19th and the Canadiens played a strong first period.
But the home team dominated the final 40 minutes, getting goals by Ryan Callahan, Tyler Johnson (shorthanded) and an empty-netter by Montreal native Alex Killorn.
Carey Price made 30 saves and was the game's First Star.
The Canadiens had 26 shots on Ben Bishop.
The win lifted Tampa Bay past the Canadiens into second place in the Atlantic Division.
Good news: Losses by Washington and New Jersey clinched a playoff berth for the CH.
Bad news: Douglas Murray almost certainly will be suspended for a late-game elbow on Mike Kostka.
Shortie is winner
With the Canadiens on a power play, the puck skipped on Andrei Markov and onto the stick of Tyler Johnson, who beat Carey Price to break a 1-1 tie.
Alex Killorn's empty-netter made it 3-1.
Lightning outshot the Canadiens 12-6, 33-26 on the game.
One scored, one disallowed
Taking advantage of a screw-up at the Canadiens blueline, Ryan Callahan lifted a backhander past Carey Price during a Tampa Bay power play.
Price later made a miraculous save on Teddy Purcell.
Purcell scored at the end of the period, but the goal was disallowed because J.T. Brown was in the crease and interfered with Price.
Replay showed no interference.
Another great night for Chris Lee.
Shots were 11-10 for the home team.
CH break on top
Teddy Purcell hit the goal post behind Carey Price, and the Canadiens goaltender made five frantic stops during a hectic sequence.
Canadiens took almost seven minutes to get their first shot on goal.
But the only goal of the period was scored by Brendan Gallagher, who got his 19th by tipping a loose puck past Ben Bishop.
Shots were 10-10.
It's likely the Canadiens and Tampa Bay will hook up in the first round of the Eastern Conference playoffs.
Still to be determined is home-ice advantage.
The Tuesday tilt is a classic four-pointer: Canadiens sit second in the Atlantic Division, two points ahead of TB, but the Lightning have a game in hand. Both teams have been hot in their last 10: The Canadiens are 8-2, TB 7-1-2.
This is the last regular-season game between the teams. All three meetings to date have gone to Overtime, and two were decided by Shootouts. TB has been on the long end of two of the 2-1 final scores.
We're talkin' tight, and this should be a good one.
Likely Lightning lines: Purcell-Stamkos-Brown, Palat-Filppula-Callahan, Killorn-Johnson-Kucherov, Malone-Thompson-Crombeen.
For the Canadiens, Lars Eller has moved onto the third line with Daniel Brière and Brian Gionta. Rene Bourque is bumped down to the fourth line with Ryan White and Michäel Bournival.
Puck drops 7:40ish.
Check back later for live game blogging.