The Jets took a first period lead before the Canadiens replied with four straight goals to take the Jets out of the contest.
Max Domi added a goal and an assist for Montreal, who rebounded from Saturday's 4-3 road loss to the Edmonton Oilers with a win.
Brendan Gallagher and Nick Suzuki each had a pair of assists.
Carey Price turned aside 27 shots for the Canadiens, who moved to 18-13-6.
Kyle Connor and Patrik Laine scored for the Jets (21-14-2).
Mark Scheifele had a pair of assists in the loss for Winnipeg.
Laurent Brossoit made 42 saves for the Jets Patrik Laine appeared to have scored 9:20 into the first to stake Winnipeg to a 1-0 lead but the play was successfully challenged as being offside via video review.
“It’s a bummer," said Jets captain Blake Wheeler of the disallowed goal. "Those definitely go against us. We gotta put an emphasis on staying onside I guess. It’s too bad. It was a heck of a goal. Real pretty, great play by those guys. That one hurts to come back. Game changed in the third period.”
Kyle Connor scored at 11:30 to make it 1-0 Winnipeg, shovelling a rebound off a Mark Scheifele shot past Montreal goaltender Carey Price.
The goal was his 15th of the season.
The Canadiens tied the contest on the power play at 15:06 when Nick Suzuki hit Thomas Tatar with a cross ice pass and the Montreal winger wired a shot past Winnipeg goaltender Laurent Brossoit, beating him high glove side to make it 1-1.
The goal was his 14th of the season.
Phillip Danault capitalized on a puck handling blunder by Brossoit to make it 3-1 Montreal 4:37 into the second.
The Jets goaltender went to play the puck along the end boards when Brendan Gallagher pounced on the loose puck before getting a quick backhand shot on goal.
Gallagher followed up, chasing his own rebound down before firing a second shot which Brossoit stopped before kicking the disc into the air which Danault adeptly bunted into the net.
Danault scored his second of the night just under the nine minute mark when he used a half shaft grip on his stick and slid the puck in between Brossoit's legs to make it 4-1 Montreal.
The goal was his 10th of the season.
Patrik Laine pulled the Jets to within a pair at 16:14 when he took a Mark Scheifele feed before moving in and wiring a low wrister past Carey Price to make it 4-2.
The goal was his 14th of the season.
The Jet winger extended his goal scoring streak to six games.
Max Domi restored the three goal cushion with 4o seconds remaining in the second after he snatched up his own rebound off a wraparound attempt and snapped a high wrister past Brossoit to make it 5-2.
The goal was his 9th of the season.
Artturi Lehkonen added an insurance marker to extend the Canadiens lead to 6-2 at 11:08 of the 3rd after Max Domi made a couple of nifty moves before feeding Lehkonen who had a wide open net to shoot at.
Montreal Head Coach Claude Julien thought his club played a solid game once they found their drive.
"Well absolutely, I thought we really had a hard time finding our legs in that first ten minutes and they were taking the play to us. We got a break there on that offside and they still scored but somehow you know we got a goal back and then we got a second one. So it just seemed that the second half of the first we started finding our legs and I thought we started playing better," he said.
"The rest of the game I thought you know the second period I thought we had a really good second and in the third we played a really smart third period. When you know when you're playing on our toes, we weren't gambling, we were regrouping and reloading extremely well. We didn't give them (Jets) any life and I think that was important."
Jets Head Coach Paul Maurice didn't spend a whole lot of time dissecting the contest.
“Listen, we came out ready to play tonight, and we played a real good game. Then we had two, three things go away from us and it was tough, and then we had no legs from that point on. We’ve had real good battle back. LB knows he’s not coming out of that game, get back in and fight your way through it. A couple of tough turnovers, we weren’t good after that. They deserve the win. It’s 2 points, not 12, fortunately," he said.
"Sorry. We won’t be doing any video. We’ll start fresh. Nobody’s carrying that with them. It was a tough night tonight, We’ve had a bunch of good nights, That was a tough one," he added.
SHOTS-MONTREAL 48 WINNIPEG 29