Jordan Weal had a goal an assist for the Canadiens, who moved to 42-29-8 on the season.
Joel Armia and Jeff Petry also scored for Montreal.
Carey Price picked up the win for the Canadiens turning aside 23 shots.
Matthieu Perreault scored Winnipeg's lone goal.
The Jets dropped their third straight game to round out their regular season home schedule.
Winnipeg remains atop the NHL's Central division with 94 points but has company atop the standings.
Nashville also has 94 points and the St. Louis Blues have pulled to within two points of both of them with 92 points.
The Jets finish off the NHL regular season with a four game road trip beginning Monday in Chicago.
Montreal is fighting to get a playoff spot as they currently 9th in the NHL's Eastern Conference with 92 points, tied with the Colombus Blue Jackets, who hold down the playoff spot on goal differential.
Montreal's schedule doesn't get any easier either.
They play Tampa Bay on Tuesday.
Connor Hellebuyck took the loss for Winnipeg, stopping 41 shots.
Montreal scored eight seconds into the first power play of the contest when Joel Armia snapped a shot past Winnipeg goaltender Connor Hellebuyck to complete a neatly executed three-way passing play at 17:05.
Jordan Weal got the puck at the top of the right faceoff circle before hitting Phillip Danault with a crisp pass at the side of the net.
Danault relayed the disc to Armia in the slot, who snapped a wrister past Hellebyck to score his 12th of the season.
The Jets failed to generate much offence in the contest but Kevin Hayes came close to scoring late in the second when Patrik Laine fed him a beautiful pass off a rush which the Jet centreman snapped past Carey Price but ended up grazing the right goalpost with.
The miss proved costly as the Canadiens scored shortly thereafter when Jeff Petry put the Canadiens ahead 2-0 at 19:23, blasting a slap shot from the left point that went in off of Jets defenceman Nathan Beaulieu's leg past a screened Hellebuyck.
The goal was his 13th of the season.
Matthieu Perreault got the Jets on the board 11:24 into the third period, pouncing on a Jack Roslovic feed in the slot before pivoting and firing the disc past Canadiens goaltender Carey Price.
The goal was 15th of the season.
Jordan Weal added an empty netter with 15 seconds left in regulation to make it 3-1 Montreal.
"That was a full sixty minute effort," said Weal. "We kind of saw by the shot count throughout the game. Limiting their zone time and creating a lot for ourselves.
Jets captain Blake Wheeler said things are tight at this point of the season.
"Well, we’re trying to win a Central Division," he said. "You know, it might come as a surprise but those guys get paid too, they’re NHL players. So as bad as we want to blow everyone out of our building and beat them 5-0, it’s not reality sometimes. You know, it's not easy for us right now. Facing some adversity right now. We're going to be a better team once we get through it."
Jets Head Coach Paul Maurice said there wasn't a lot to like about the game.
“We didn’t like our game. So many of the important things that are important to us that we need to do to function as a team – our gap (was) way off. Lots of ice for them, especially early in the first period and through the second, they came through our neutral zone so very easily. Which would be the opposite of the way that we like to play. We had very little sustained play in the offensive zone. And we’re there, we’re at the puck, but we don’t get it and it’s coming back the other way. We had a hard time getting contain and getting stops and doing what we do well with our movement. Early on especially, a bunch of the pucks we put at the net, we were a long ways from being net front on that. We got better in parts as the game went on, but it was a game that doesn’t look like the style of game that we like to play.”
Canadiens Head Coach Claude Julien said his club did what they had to do.
“I thought right from the get-go we were prepared and made good, solid passes, good decisions. Our defensive game was really good. Our (defencemen) were doing a great job of really having a tight gap and forcing them not to come in easily on the rush."
“I thought we forced them to dump a lot of pucks. Our goaltender is like our third. I thought he did a great job at moving the pucks tonight.”
SHOTS-MONTREAL 44 WINNIPEG 24