J.T. Miller scored, and Braden Holtby made 20 saves for the Canucks (19-22-3), who are 1-4-0 in their past five games.
Vancouver trails Montreal by 10 points for fourth in the division with four games in hand. The top four teams will qualify for the playoffs.
"I thought we got better as the game went on, but a couple of mistakes ended up in the back of our net," Canucks forward Tanner Pearson said. "That's going to happen against this team, so we've got to minimize those. They control the puck pretty well. We need to get more shots and recover the pucks and start generating that way. That will be a focus point for us and a good place to start."
William Nylander gave Toronto a 1-0 lead at 15:29 of the first period when he took a pass from Alex Galchenyuk following a turnover by Quinn Hughes and shot under Holtby's pad.
Matthews scored 51 seconds into the second period to make it 2-0, one-timing a pass from Marner on a 2-on-1. He leads Connor McDavid of the Edmonton Oilers by eight goals.
"He's one of the best goal-scorers I've ever played with, and I've only played one game with him," Hutton said. "It's pretty fun to watch. If he gets a chance, he buries it. I was talking with a few teammates, and honestly every time he comes down and shoots, your eyes get big and think, 'Oh, that's a goal.' So it's pretty fun to watch."
Pierre Engvall extended the lead to 3-0 at 2:56 of the second. He received a pass low in the right circle from Jason Spezza on a rush and beat Holtby short side over his glove.
Miller scored on the power play at 15:36 to cut it to 3-1.
Marner made it 4-1 at 19:05 of the third period when he beat a scrambling Holtby with a one-timer after Alex Kerfoot intercepted a clearing attempt from the goalie along the left boards.
"It was a tight game," Canucks coach Travis Green said. "I thought the compete level was high for both teams having played on Wednesday (Vancouver lost to the Ottawa Senators 6-3). We definitely got better as the game went on. There were a couple plays we'd like to have back for sure, but I thought their skill made a couple plays for them that was probably the difference at the end of the night."
NOTES: Matthews scored his 11th game-winning goal of the season, tying Tod Sloan (1955-56) for the second most in Maple Leafs history. Charlie Conacher scored 13 in 1934-35. ... Canucks forward Kole Lind had two shots, one hit and one block in 17:12 in his NHL debut. … Hutton had one hit and three blocks in 22:04 in his Maple Leafs debut after being acquired in a trade with the Anaheim Ducks on April 12. ... Toronto played without forward Nick Foligno, defensemen Morgan Rielly and Jake Muzzin, and goalie Jack Campbell, each out because of maintenance.
