Phillip Danault, Max Domi and Brendan Gallagher scored in regulation for the Canadiens, who snapped a two-game skid despite giving up a 3-0 lead. Tomas Tatar had two assists.
''We haven't been good with leads,'' Gallagher said. ''We have to work through this and learn to play with the lead.''
It was the fifth consecutive home game in which the Canadiens failed to protect a multigoal cushion, and are 1-2-2 in those games.
''We were better tonight,'' Gallagher said. ''We were more aggressive. But at the same time, three pucks still end up in the back of our net. You have a two-goal lead or a three-goal lead, they need to be locked down.''
Charlie Lindgren made 27 saves in his first start since Feb. 4, when he won 5-4 in a shootout in New Jersey. Carey Price got the night off after playing 11 consecutive games.
''Lindgren played a good game,'' coach Claude Julien said. ''There was a lot of traffic in front of him on their goals. He made some big saves, especially in the dying seconds.
''I'm pretty sure you're going to see him again. The goal is not to ride Price into the ground. The goal, as you saw tonight, is to give Charlie the opportunity to play here. And if he plays well, why not?''
Haydn Fleury, Joel Edmundson and Justin Williams scored for the Hurricanes, who forced overtime after being down 3-0.
''We can't chase games,'' Williams said. ''Chase and chase and chase. It's exhausting. Our urgency from the start of the game just has to be better. It's just a mental thing.
''Sometimes maybe you have to trick your mind to think you're down a goal to start the game.''
Carolina's goaltending troubles continued with both James Reimer (lower body) and Petr Mrazek (concussion) injured last week in Toronto. Backup Anton Forsberg, who also played Friday, allowed three goals on 20 shots before being pulled in the second period. Alex Nedeljkovic stopped 18 of 19 saves in relief.
The only goal Nedeljkovic let in was to Petry in overtime on a breakaway.
The Canadiens had blown two-goal leads in their previous four home games (0-2-2), and they again didn't make it easy on Bell Centre fans.
''It would definitely be a much different feeling in here if we were to lose in overtime, especially with the lead that late in the game,'' said Petry, who scored his 10th of the year. ''It's a sense of relief to get the win. But we have to figure out a way to end it in regulation. We have to have that killer instinct, that mentality.''
Edmundson made it 3-2 at 1:14 of the third when his wrist shot from the blue line soared into the top corner of the net. Andrei Svechnikov was screening Lindgren on the play.
After a back-and-forth third, Williams tied it for Carolina with 1:17 remaining by deflecting Edmundson's point shot.
The Canadiens were leading 8-0 in shots when Danault completed a nice passing play from linemates Tatar and Gallagher to slide the puck five-hole on Forsberg. With the assist, Tatar set a career high with 59 points.
Montreal started the second period with similar energy to the first and scored twice within 17 seconds to take a 3-0 lead.
Domi capitalized on a scramble in front of Forsberg for his fourth goal in as many games at 3:46. With fans still cheering for Domi's goal, Gallagher fired a one-timer on a rebound from Tatar at 4:03 to end Forsberg's night.
The Hurricanes got one back when Fleury threw a puck on net from the point that found its way through a couple of bodies and under Lindgren's glove at 7:45.
With Williams in the penalty box for slashing, Lindgren denied Vincent Trocheck on the short-handed breakaway with five minutes left in the second.
NOTES: The Hurricanes are one point behind Columbus for the second wild-card spot in the Eastern Conference. ... Montreal improved to 14-16-6 at home this year. ... Canadiens D Xavier Ouellet returned after missing three games with a concussion. ... Montreal snapped a three-game losing skid against Carolina.
Hurricanes: at Philadelphia on Thursday night.
Canadiens: at New York Islanders on Tuesday night.
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