"I had a good feeling," Sutter said. "I trust that group inside the room. I had good vibes coming to the rink today that we were going to play a really good game. We had a tremendous effort from our goaltender right out."
Brian Gionta and John Madden also scored as the Devils, winners of three of four, quickly put to rest any bad memories from the 4-2 loss to the Stars.
Continuing his strong play since Martin Brodeur went down with a biceps injury, Clemmensen again came up big for the Devils.
"We kind of had a big letdown in Dallas, especially in the second period," Clemmensen said. "This is a team that expects to come and win every night. Collectively as a team and a coaching staff, we don't want to let anything slip. Playing here at home against a good Montreal team, it was good for us to get back to playing our game."
Max Pacioretty scored in his NHL debut for Montreal, which had won three straight.
"I'm glad to get the first one out of the way," Pacioretty said. "I know I have to play a lot better to stick around here. I think I'll be able to play better now that I got the first one out of the way. I wasn't handling the puck too well. Maybe it was the nerves."
The Canadiens entered the game missing a lengthy list of injured players: Carey Price, Alex Tanguay, Christopher Higgins, Saku Koivu, Georges Laraque and Mathieu Dandenault.
With Price sidelined, Jaroslav Halak made his first appearance in goal against New Jersey. He lasted two periods, giving up 3 goals on 22 shots. Marc Denis finished up for Montreal.
"Giving them three goals and the lead makes it really hard," Canadiens coach Guy Carbonneau said. "I'm sure Jaro wished he had a few back, but it's too late now. When that team is up by one or two goals, it's really hard to come back on them."
Gionta and Parise scored first-period goals as the Devils took a 2-1 lead. Gionta opened the scoring at 14:21 with a hard drive from the top of the right circle.
Pacioretty celebrated his NHL debut by zipping around Devils defenseman Andy Greene to beat Clemmensen at 16:30, tying the score at 1.
Parise restored the Devils lead with 1:35 remaining as New Jersey cashed in on a turnover by Montreal defenseman Andrei Markov in his own zone. Parise, on a feed from Langenbrunner, beat Halak from the bottom of the right circle for his team-leading 22nd goal.
In the second, Madden put New Jersey up 3-1 at 11:11.
Parise returned the favor at 13:11 of the third, threading a pass to Langenbrunner in the slot for the goal that put New Jersey ahead 4-1.
Notes: Brodeur has begun off-ice workouts as part of his recuperation from biceps surgery. The Devils hope to have him back in goal in February or March. Clemmensen, assuming the bulk of the workload in his absence, made a 10th straight start. ... Montreal called up Denis, Pacioretty and Kyle Chipchura and Yannick Weber from Hamilton (AHL) on Thursday. Weber was only one who did not dress against New Jersey ... Devils D Colin White missed a third straight game with an upper body injury. ... Pacioretty was Montreal's first round pick in the 2007 draft. ... The game attracted 17,625, the Devils' third sellout of the season. The other two sellouts were visits by the New York Rangers.