John Tavares scored and Erik Kallgren made 24 saves for the Maple Leafs (47-19-6), who reached 100 points for the sixth time. Toronto is 7-0-1 in its past eight and leads the Boston Bruins by five points for second place in the Atlantic Division.
"It's a great accomplishment for our team and with 10 games left, it's a sign you've had an excellent regular season," Toronto coach Sheldon Keefe said. "We've been preparing and acting, feeling as though we're a playoff team for a long period of time now but certainly to have that official speaks to the process and the work that the guys have put in to this point. And also it just allows us to zoom in and focus even more so on making sure that our game is ready and our team is prepared when the time comes."
Jake Allen made 14 saves for the Canadiens (20-41-11) before leaving 13:32 into the first period with a lower-body injury. Sam Montembeault made 23 saves in relief.
"We came out a little slow, a little sloppy and obviously they capitalized on the turnovers there on the second goal," Canadiens forward Josh Anderson said. "I thought we played pretty good later on in the first period and then carried over to the game and we had some big kills there that kept us in the game and when Montembeault came in, he played phenomenal and gave us a chance to win."
Matthews put Toronto up 1-0 at 13:32 of the first period when he backhanded a rebound from Mark Giordano's shot over Allen's outstretched left pad.
Matthews then made it 2-0 at 13:59 when he cut into the slot and shot past Montembeault's glove from the left hash marks for his NHL-leading 58th of the season.
"When the second one goes in, (Jason) Spezza turned around (on the bench) and gave me the eyes like there's something special here and no doubt, it's fun," Keefe said. "I'm surprised he stopped too to be honest with the way he was playing, it felt like he was going to have a serious night. But he was great tonight. For him to establish the (Toronto record for goals in a season) and come back home here, he's clearly not satisfied so he's continuing to push himself and our team."
Joel Edmundson cut the lead to 2-1 at 5:58 of the second period, one-timing a pass from Nick Suzuki in the slot.
Tavares made it 3-1 at 8:07 when he spun from the right face-off dot and banked a shot off Jordan Harris' skate at the side of the net.