Oliver Kapanen, Lane Hutson and Phillip Danault scored for the Canadiens.
Samuel Motembeault turned aside shots for Montreal, who moved to 32-17-8.
Kyle Connor scored the lone goal for the Jets, who dropped to 22-26-8.
Connor Hellebuyck made 22 saves for Winnipeg, who lost their last game before the Olympic break.
Winnipeg opened the scoring just over six minutes into the first on the power play.
Gabriel Vilardi took a Mark Scheifele feed on the side of the net before hitting a wide open Connor inside the right side faceoff circle. The Jet winger snapped the disc past Motembeault, beating him low blocker side to make it 1-0 Jets.
The goal was his 25th of the season.
Oliver Kapanen tied it 16:26 into the first when he scooped up a rebound off a point shot from Oliver Kapanen and fired it past a sprawling Hellebuyck to make it 1-1.
Montreal took the lead in the second period when Josh Anderson tipped a Jayden Struble shot past Hellebuyck 5:28 into the period.
The goal was his 12th of the season.
Lane Hutson made it 3-1 6:44 into the second when Josh Anderson gained the blue line before sending Hutson in alone on Hellebuyck.
The Canadiens defenceman took the pass on his backhand before switching to his forehand and beat the Winnipeg netminder with a high shot to score his 10th goal of the season.
With Josh Morrissey off for slashing Brendan Gallagher sealed the win with a power play marker 10:57 into the third, converting a Kirby Dach feed to make it 4-1 Montreal.
The goal was his 6th of the season.
Phillip Danault added an empty netter with 13 seconds left in regulation.
SHOTS-MONTREAL WINNIPEG
ATTENDANCE-15,225
