The win was their second in a row.
Winnipeg jumped to a four-goal first period lead only to have the Canadiens answer with the next four, including a hat-trick by Josh Anderson to tie up the contest by early in the second period.
The Jets responded by scoring three power play markers of their own to take control of the contest which featured seven tallies by the end of the first period.
Evgeni Svechnikov, Nate Schmidt, Adam Lowry and Andrew Copp each had a goal and an assist for the Jets.
Kyle Connor and Blake Wheeler each had two assists.
Connor Hellebuyck made 31 saves for Winnipeg, who moved to 24-21-9.
Josh Anderson had three goals for the Canadiens. The hat-trick was the first of his career.
Artturi Lehkonen also scored for Montreal, who dropped to 13-34-7.
Sam Montembeault and Andrew Hammond combined to make 22 saves for Montreal, who lost the first game of a four-game road trip.
The Jets struck for four goals before the Canadiens replied with their first as Evgeni Svechnikov got his stick on a Nate Schmidt centering pass 5:21 into the contest to give Winnipeg an early lead.
Nate Schmidt made it 2-0 36 seconds later when Pierre-Luc Dubois found him alone at the point and hit him with a crisp pass at the point the defenceman promptly fired between Montembeault's pads to score his 4th of the season.
Adam Lowry converted a Dylan DeMelo feed off the rush, beating Montembeault with a neat backhand deke to give the Jets a three-goal cushion.
The goal was his 7th of the season and his 4th goal in his last six games.
Mark Scheifele made it 4-0 27 seconds later when he one timed a Pierre-Luc Dubois feed past Montembeault from the slot, beating him high glove side.
The goal was his 19th of the season.
Josh Anderson got the Canadiens on the board at the 11:18 mark when he caught Jets goaltender Connor Hellebuyck napping, squeezing the puck between his pads from the side boards.
Anderson scored again at the 17 minute mark on the power play when he knocked a rebound past Hellebuyck off a Cole Caufield shot from the point to make it 4-2.
Anderson scored his third of the contest 4:08 into the second when he converted a Ryan Poehling feed, waiting patiently for Hellebuyck to expose the top of the net before snapping a shot just under the cross bar.
The goal was his 15th of the season and his first career hat-trick.
Rem Pitlick was unsuccessful on a penalty shot awarded just under the 17 minute mark of the second period when Pierre-Luc Dubois slashed him on a breakaway.
Andrew Copp restored the Jets lead on the power play 18 seconds later at 17:17 when he took a Neal Pionk pass along the side boards before moving in and beating Montembeault just inside the far post.
The goal was his 11th of the season.
Mark Scheifele potted his 2nd of the night and 20th of the season at 2:46 of the third when he banked the puck in off of former teammate Ben Chiarot's skate from behind the goal line.
The goal was his 20th of the season.
With Brendan Gallagher off for high sticking Pierre-Luc Dubois converted a Mark Scheifele feed, snapping a wrister past Montembeault's glove 5:49 into the third.
The goal was his 22nd of the season.
Canadiens Head Coach Martin St. Louis had seen enough and pulled him in favor of Andrew Hammond.
Paul Stastny rounded out the scoring at 17:26 when he finished off a three-way play converting an Adam Lowry feed to make it 8-4.
Montreal vists Calgary Thursday while Winnipeg hosts Dallas Friday.
SHOTS-MONTREAL 35 WINNIPEG 30
ATTENDANCE- NOTES-The game marked the 5th time this season the Jets surpassed the 6 goal mark.
8 Winnipeg forwards had two or more points in the win over Montreal.