Patrik Elias, Paul Martin and Johnny Oduya each had a multi-point effort for the Devils, who have won five in a row and head into the All-Star break atop the Atlantic Division with a 29-15-3 record and 61 points, one more than the Rangers. John Madden notched two assists, while Scott Clemmensen made 26 saves.
Matt D'Agostini scored a goal and picked up an assist for the Canadiens, who have lost two straight and find themselves in second place in the Northeast Division with a 27-13-6 record and 60 points, 11 behind the Boston Bruins.
Carey Price, the Eastern Conference starting netminder for Sunday's All-Star game at the Bell Centre in Montreal, made his first start since suffering an ankle injury in a December 30 game against Tampa Bay. The fifth overall pick of the 2005 draft, Price was beaten four times on 33 shots.
New Jersey grabbed a 1-0 lead with 8:08 remaining in the first period. Martin exited the penalty box, and a long pass from Elias sent the Devils defenseman on a breakaway. Martin skated down the slot and zipped the puck through Price's legs for his fourth of the season.
Travis Zajac drove hard to the net and jammed home a rebound off a Parise shot behind Price 6:18 into the middle stanza, then Josh Gorges countered for Montreal with 6:04 left in the frame.
Clemmensen made a magnificent save on Saku Koivu, but got tangled with teammate John Madden and couldn't get over to stop Gorges' follow-up chance.
A laser by Oduya from the top of the left circle made it 3-1 with 1:40 to go in the second, and Parise tallied at 2:05 of the third period.
D'Agostini cut the deficit to 4-2 on the power play at 7:46 and Elias added a shorthanded empty-net goal in the final minute to cement the win.