Cole Caufield scored his third NHL goal for the Canadiens (24-20-9), who lost 5-1 to the Ottawa Senators on Wednesday.
Cayden Primeau started but was pulled after allowing four goals on 15 shots in the first period. Jake Allen made 18 saves in relief.
"I talked to him in the dressing room quick, just me and him," Allen said of Primeau. "It's a bump in the road for him. I can tell how good a goalie he is and how good a kid he is. Once Carey Price's legacy goes, Cayden is going to be the guy here. You have to fail to succeed in this league, especially as a goalie. I'm sure he's going to take it hard, as all young guys do, I would have done the same thing. But he's going to move on and be ready to go for us, we're going to need him again."
The teams play again here Saturday. The Canadiens lead the Calgary Flames by 10 points for the final playoff berth in the North Division; Calgary has two games in hand. The Vancouver Canucks trail Montreal by 16 points and hold five games in hand.
Montreal could have clinched a playoff berth win a win and a win by the Edmonton Oilers against the Canucks.
Alex Galchenyuk gave Toronto a 1-0 lead 16 seconds into the first period with a backhand from the slot. Tavares made it 2-0 at 3:24 when he put in a rebound of Jake Muzzin's shot at the side of the crease.
The Maple Leafs led 3-0 at 10:38 after Pierre Engvall put in his rebound from just above the goal line below the left face-off circle.
Marner made it 4-0 at 17:21 when he took a pass from Joe Thornton, who was positioned along the boards inside the blue line. The assist extended Thornton's point streak to seven games (two goals, five assists).
"That first period was just the guys buzzing," Campbell said. "Right out of the gate we had a great start, and I love seeing that. Obviously it gives the team a ton of confidence. You need a good start like that to beat Montreal."
Caufield cut the lead to 4-1 at 13:30 of the second period with his first NHL goal not scored in overtime (seven games). Artturi Lehkonen made it 4-2 at 3:04 of the third period.
"They jumped all over us," Canadiens defensemen Ben Chiarot said. "We were slow out of the gate and they came out pretty quick and we spotted them a couple of goals. It's an uphill battle from there, and on a back-to-back situation, that's not easy. That wasn't Primeau's fault, it's our fault, we were flat in front of him and didn't give him any help. Young goalie going in (21 years old), we have to be sharp early on and let him find his groove."