Jesperi Kotkaniemi and Josh Anderson also scored for the Canadiens. Carey Price, playing in his 700th game, made 34 saves - including several strong ones in the third period as the Jets pressed for the equalizer.
''He stood in there all night for us and played absolutely amazing,'' Anderson said. ''What a milestone for him tonight to get that win.''
Kyle Connor scored two power-play goals for Winnipeg (17-9-2). Connor Hellebuyck stopped 27 shots and denied Brendan Gallagher on a penalty shot in the second.
Winnipeg pulled Hellebuyck for an extra attacker with about two minutes left, but Toffoli put the game away at 19:12.
Montreal ended its two-game slide and improved to 13-8-7 halfway through the condensed 56-game schedule.
Price made a great left toe save on Paul Stastny's redirect early in the third with Winnipeg on the man advantage. He gave up a power-play goal to Connor on a blistering one-timer at 5:47, but held the Jets in check from there.
''When he gets feeling good, it seems like nothing is going by him,'' Canadiens defenseman Josh Kulak said. ''It's nice having him back there. He's a leader on our team and he sets the tone when he makes some big saves.''
Winnipeg remained four points behind first-place Toronto in the North Division standings. The Jets have two games in hand on the Maple Leafs. Montreal is alone in fourth place with 33 points.
Montreal improved to 8-3-6 on the road, while the Jets fell to 9-5-1 at home.
''It was just a tight game,'' Winnipeg coach Paul Maurice said. ''There was broken plays, flurries to the net at both ends, but not a tremendous amount of sustained (offensive) zone time.
''I think that's a function of both teams competing pretty hard defensively.''
The Canadiens announced earlier in the day that defenseman Ben Chiarot is expected to miss six to eight weeks after undergoing surgery to repair a broken hand.
The teams play again Wednesday night. Then the Canadiens open a six-game homestand Friday night against Vancouver, and the Jets begin a seven-game trip Thursday night at Edmonton.
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