Brodeur was pleased to see Parise's efforts rewarded.
"He's been playing well lately," Brodeur said. "He's Johnny on the spot. He puts himself in good positions to score goals. Right now, he has the hot stick. Let's hope it keeps up."
Parise had a goal in every period to raise his team-leading total to 12. He also assisted on Brian Gionta's power-play goal in the third to help the Devils beat the Canadiens for the ninth straight time.
Parise opened the scoring with 34.2 seconds remaining in the first on a play that started when a cross-ice pass hopped over Montreal defenseman Patrice Brisebois' stick. Parise broke into the Montreal zone and slipped a backhander past Carey Price.
Brodeur was stellar early in the opening period when the Devils picked up three quick penalties. He turned aside Tomas Plekanec's drive off the right wing, made a solid stop on Mark Streit's slapper from the point and denied Saku Koivu's backhander in the slot to keep the game scoreless.
Aided by the power plays, Montreal had 13 of the first 14 shots.
"After that flurry, we took over the game," Brodeur said. "We were able to get through it. Then we got a break to score a goal and that was big."
In the second, Parise gave the Devils a two-goal cushion with a power-play goal at 13:10.
The Canadiens wound up penalty trouble in the third when Guillaume Latendresse and Kyle Chipchura picked up concurrent double-minor penalties for high-sticking at 5:48. The Devils cashed in twice on the extended five-on-three, getting goals from Parise at 6:22 and Gionta at 7:49
"They got a few bounces that maybe we didn't," Price said. "They had pucks on their sticks looking at open nets a couple of times. That's part of the game."
Devils ironman Jay Pandolfo missed the game because of a groin injury, ending his streak of consecutive games at 307. ... Montreal native Brodeur is 34-12-5 against the Canadiens.
Copyright by STATS LLC and The Associated Press
Arena: Prudential Center Location: Newark, New Jersey
Referees: Michael McGeough, Brad Watson Linesmen: Shane Heyer, Jonny Murray
Attendance: 15,081 (85.6% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Zach Parise (10)
Zach Parise (11)
(Power Play) Assists: Brian Gionta, Travis Zajac
Zach Parise (12)
(Power Play) Assists: Jamie Langenbrunner, Paul Martin
Brian Gionta (9)
(Power Play) Assists: Zach Parise, Jamie Langenbrunner