Josh Morrissey, Trevor Lewis, Nikolaj Ehlers and Andrew Copp scored for Winnipeg.
Connor Hellebuyck picked up the win for the Jets, who moved to 24-13-3.
Phillip Danault and Paul Byron scored for Montreal (17-11-9), who have lost their last two games.
Josh Morrissey scored 18 seconds into the game, firing a wrister in off the post off a rush.
Montreal replied 1:22 later when Phillip Danault knocked a rebound past Hellebuyck after he made a stop on a Tomas Tatar effort.
Trevor Lewis made it 2-1 just over the eight minute mark when he redirected a hard Neal Pionk feed past Jake Allen.
The goal was his 2nd of the season.
Nikolaj Ehlers gave the Jets a two-goal lead at 13:07 when he burst down his wing and beat Allen with a wrister.
Paul Byron capitalized when Hellebuyck got caught behind his goal when the puck took a strange bounce and found him with the puck on his stick.
He one timed the disc into the goal to make it 3-2.
The Canadiens pulled their goaltender with about 90 seconds remaining in regulation but were unable to get the equalizer.
Andrew Copp potted an empty netter to seal the win for the Jets.
The two teams face each other again Saturday night in Montreal.
SHOTS-WINNIPEG 27 MONTREAL 38