J.J. Moser would score his first-ever playoff overtime game-winning goal. Tampa ended their skid of seven straight overtime playoff game losses with the thrilling win.
The Lightning outshot the Habs 9-0 in overtime.
Recap & Highlights
Montreal would force the momentum in their favor in the first half of the opening period, holding Tampa Bay to zero shots on goal in the first 10 minutes.
But it would still be the Lightning who would get on the board first.
Brandon Hagel would score on Tampa's first shot on goal of the game to put his squad up 1-0.
It marked Hagel's third goal of the playoffs already, while Jake Guentzel picked up his fourth assist. It is now the 15th time the Lightning have scored on their first shot - the most of any NHL team since 2010.
Both teams would find themselves in an almost full-out team brawl that would eventually give the Canadiens a power play - and they capitalized.
Lane Hutson would send one past Andrei Vasilevskiy almost from the blue line to tie things up 1-1 with his first career playoff goal.
Nick Suzuki and Cole Caufield both put up their third assists of the playoffs.
It would take just a couple more minutes before the Habs would go back on the power play for the remainder of the first period.
Both teams would combine for 30 total penalty minutes in the first period alone, with 12 players total being sent to the sin bin (Yanni Gourde and Corey Perry went twice for Tampa).
Gourde was assessed his second of the game after the first period whistle, giving the Habs their third power play chance of the game right out of the gate for the second period, but they couldn't get anything done.
The scrums wouldn't stop as both teams were out for more than blood. Hagel and Montreal's Game 1 star Juraj Slafkovsky would drop the gloves as both received five-minute majors for fighting.
With 1:24 left to go in the second, the Habs would finally get on the board again.
Josh Anderson, who scored the first goal in Game 1, would put Montreal up 2-1 with their second straight goal.
Anderson joined Jesperi Kotkaniemi as the second Habs player in the past 15 years to score in each of the team's first two playoff games.
Montreal, whose power play was 1-for-3 through the first two periods, would go on the PP for the fourth time with 40 seconds left, giving them a man advantage to start the third, but nothing comes of it.
Even if tempers calmed down in the second, both teams would head into the final frame with a combined 46 penalty minutes.
Kucherov had gone 16 playoff games without a single goal - that all came to an end on Tuesday evening.
The Lightning's star would tie things up 2-2 with a wrap-around with 7:27 left to go in the third.
Kucherov now has the fourth-most game-tying goals (29) in the playoffs of a non-USA-born player, sitting behind Jaromir Jagr (47), Alex Ovechkin (34), and Evgeni Malkin (33).
With 2:15 left in the third, Scott Sabourin (TB) was originally called for a five-minute major for interference, but after review, it was downgraded to a two-minute minor as the Canadiens couldn't pull through with a golden opportunity.
And it would come back to bite them as Moser would send home the game winning to even the series.