Max Pacioretty scored twice and Andrei Markov and Jeff Halpern also scored for Montreal (23-7-5), which swept the season series against Carolina and remains undefeated in 10 games against the Southeast Division this season.
The win allowed Montreal to restore a three-point lead over the idle Boston Bruins in the race for the Northeast Division title. Boston holds a game in hand.
After the Canadiens were unable to convert on a couple of quality chances in the opening minutes of the first period, the Hurricanes took advantage to break the ice on a delayed penalty call against Montreal.
Markov evened up the score on the power play at 15:03 with a slapshot from the right point. P.K. Subban, fresh off being named the NHL's second star of the month for March, added an assist on the play, tying him with Pittsburgh's Kris Letang and Minnesota's Ryan Suter for the league lead in points by a defenceman.
The Canadiens went ahead early in the second when rookie defenceman Nathan Beaulieu found Halpern in the slot for the veteran's first of the season. The assist was the first point for Beaulieu, who made his NHL debut on Saturday.
Jiri Tlusty nearly tied things up in the opening minute of the third, only to hit the post.
Pacioretty provided the Canadiens with some insurance at 10:58 of the third when he slipped the puck through an opening to Peters' left side. Pacioretty also added a goal into an empty net.
Habs winger Colby Armstrong had to be helped off the ice early in the third after a hard collision with Dwyer that left him favouring what appeared to be his right leg. He did not return.