They did so with the help of their stars, as Nikita Kucherov had 2 goals and an assist, while Steven Stamkos and Ondrej Palat found the back of the net. Kucherov's goals help him finish the series with six for Tampa Bay, who recovered after losses in games 4 and 5.
Palat added an assist, giving the Lightning much-needed contribution, as they were playing without Ryan Callahan. The Lightning star underwent an emergency appendectomy on Monday night.
Ben Bishop finished the night with 18 saves for Tampa Bay, outshining Montreal's Carey Price, who had 24 saves. Including the win on Tuesday, the Lightning have now won nine of eleven meetings with their division rival this season.
The Canadiens' elimination means that the last of the five Canadian teams in the playoffs has been knocked out. Montreal was the last Canada-based team to win the Stanley Cup in 1993.
The other semi-finals series saw a comeback completed in the most exciting of ways in game 7. The New York Rangers completed their comeback from a 3-1 series deficit, as Derek Stepan scored the game-winner in overtime for a 2-1 win over the Washington Capitals on Wednesday night. They advance to face the Lightning in the conference finals with the 4-3 series win.
Stepan's goal occurred at 11:24 of the overtime period on wrist shot from the left wing. They are the only team to win a series after trailing 3-1 in consecutive years, as they did so against the Pittsburgh Penguins in 2014.
Goalie Henrik Lundqvist made 35 saves en route to his sixth career game-7 win, joining just Patrick Roy and Martin Brodeur as the only goalies to do so. Lundqvist recorded 8 saves in overtime alone.
Alex Ovechkin scored to get the Capitals ahead early, as it looked to be all Washington early on. Kevin Hayes tied it at 1-apiece with a second-period tally. Braden Holtby looked good all series long and made 37 saves in the loss for Washington.
These teams have opposite success when it comes to game 7's. The Capitals are 0-5 in franchise history in those games. Meanwhile, the Rangers have now won six straight series that go into seven games, including three against the Capitals.
New York's win was their fourth overtime win in four tries, all by the score of 2-1. It was their first game-7 win in overtime since a win over the New Jersey Devils in 1994, the year they won the Stanley Cup.
Game 1 of the Eastern Conference Finals between the Lightning and Rangers is Saturday afternoon at 1 p.m. EST.