WATCH: [All Maple Leafs vs. Canadiens highlights]
"It's always a hostile environment when we come in here, and it's obviously a great atmosphere, so to come out with two points, it's what we came here to do and we're going to take it and move on here," said Matthews, who leads Toronto with eight points (five goals, three assists) in five games.
James van Riemsdyk and Patrick Marleau scored for the Maple Leafs (4-1-0), who matched their best start since 2013-14. Frederik Andersen made 31 saves, including 13 in the third period and one in overtime.
"Anytime you come in here you're playing [Price], he's the best there is in the League," Toronto coach Mike Babcock said. "It's great to look down the rink at him and you've got to beat him one on one. You've got to be better than him if you're going to win, so I thought [Andersen] did a good job tonight."
Jonathan Drouin scored his first Montreal goal and had an assist for the first multipoint game by a Canadiens player this season. Jeff Petry and Alex Galchenyuk scored for Montreal (1-3-1), which scored four goals in its first four games and has lost four straight. Price made 18 saves.