Andrei Svechnikov scored the game-winner for his second of the postseason. Although some credit Sebastian Aho with the tip-in, which would be his fourth.
This now marks back-to-back overtime wins for the Canes, who have now won seven straight in OT during the playoffs dating back to Game 5 against the New Jersey Devils last season.
Goaltender Frederik Andersen has now given up two or fewer goals in 10 of his 11 starts these playoffs. It also marked back-to-back games in which he recorded only 10 saves.
He has now recorded more than 20 saves in only one of his last five games.
Montreal fell to 3-4 in overtime this postseason. Their seven overtime games are tied for the second most in a single playoff run in franchise history, still three short of their 11 in 1993 when they were 10-1 in those games.
Goaltender Jakub Dobes recorded over 30 saves (35 total in Game 3) for the sixth time these playoffs - the Habs are now 3-3 in those games.
Recap & Highlights
The first penalty of the match came before the first goal, sending Montreal on the power play. After failing yet again, the Habs fell to 0-for-5 on the power play this series with just a total of two shots on goal.
Carolina made sure they paid for missing out on a big opportunity.
Shayne Gostisbehere scored his first goal of the postseason to put Carolina up 1-0 almost halfway into the first period.
Mark Jankowski (4) and Eric Robinson (3) picked up the assists. The Canes have now scored first in all three games so far this series.
Robinson was the one who scored first in Game 2, but Gostisbehere's is the longest that the Canes have taken to score first this series (8:24).
But eight minutes later, Montreal would make up for their earlier power play blunder and tie it up 1-1.
Mike Matheson scored his second goal of the postseason, with Ivan Demidov (6) and Jake Evans (8) picking up the assists.
The Habs need just three more game-tying goals to set a new postseason franchise record (15 in 1979).
After the Habs found some momentum, the Canes found the net for the second time in Game 2 just 54 seconds later.
Taylor Hall scored his fourth of the postseason, first of the season, to make it 2-1, with assists from K'Andre Miller (7) and Jackson Blake (8)
Once again, the Canes dominated in shots, outshooting Montreal 15-5, making it 22-7 in the first period of Game 2 and Game 3 combined.
After 4:43 into the second period, the Habs tied it up once more to make it 14 game-tying goals this postseason, needing two more to break their own franchise record.
Lane Hutson scored his third goal of the postseason, and his first in 14 games, to make it 2-2. Cole Caufield (7) and goaltender Jakub Dobes (1) picked up the assists.
Hutson became the first ever defenseman in Canadiens' history to record 10 power play points in a single postseason.
His last goal these playoffs was the Game 3 overtime winner against the Tampa Lightning in the first round.
Carolina missed out on their lone power play of the second period, while both teams failed during a 4-on-4.
Montreal was still outshot 10-6 once again as the game entered the third period.
The Habs would score what they thought would be their third of the game to take the lead, but after further review, offside was called.
It would've been Noah Dobson's first goal of the postseason and Caufield's second assist of the game.
Dobson would pick up an interference penalty moments later, putting Carolina on their third power play, which ultimately failed yet again.
With neither team capitalizing on opportunities, Carolina entered overtime for the second straight game outshooting the Habs, this time 32-12.
In the end, it was the Canes who came away with the win, outshooting them 38-12.