Adam Lowry and Vladislav Namestnikov also scored for the Jets.
Josh Morrissey had a pair of assists.
Connor Hellebuyck made 26 saves for Winnipeg to pick up his NHL leading 19th win of the season.
Lane Hutson and Josh Anderson scored for the Canadiens.
Sam Montembeault turned side 23 shots for Montreal, who dropped to 11-16-3.
Lane Hutson scored 7:48 into the first period when he snapped a wrister past Hellebuyck from the left wing circle.
The goal was his first of his NHL career.
Gabriel Vilardi tied it up on the power play 14:34.
With Kirby Dach off for high sticking, Kyle Connor slid a pass from the right corner, cross crease to Vilardi who hammered it past Montembeault to make it 1-1.
Adam Lowry gave Winnipeg the lead just over two minutes later at 16:40 when Nino Niederreiter slid him the disc from behind the Montreal net and into the crease as he curled around the Montreal net.
The goal was his 8th of the season.
Lowry fired the disc into a largely open net to make it 2-1 Jets.
The Jets went up a pair 6:26 into the second while on a two-man advantage when Kyle Connor one timed a Josh Morrissey feed past Montembeault.
The goal was his 17th of the season.
With the Jets unable to clear their zone, Josh Anderson pulled Montreal to within a goal at the 8 minute mark when he snapped a Christian Dvorak feed past Hellebuyck.
Canadiens Head Coach Martin St. Louis pulled his goaltender with just over a minute left in regulation but the Canadiens were unable to score.
Vladislav Namestnikov scored into an empty net with 7 seconds left in the third period to seal the win for the Jets.
The goal was his 8th of the season.
Montreal hosts Buffalo Tuesday while Winnipeg visits San Jose.
SHOTS-MONTREAL 28 WINNIPEG 27
ATTENDANCE-15,225
