Matthews also had assists, William Nylander added goal and an assist, and Jason Spezza, Rasmus Sandin and Alexander Kerfoot, into an empty net, also scored. Jack Campbell stopped 22 shots, and Mitch Marner had two assists.
Jesperi Kotkaniemi scored for Montreal, and Carey Price stopped 29 shots.
The best-of-seven matchup between the Original Six rivals shifts to the Bell Centre for games Monday and Tuesday nights. The Canadiens won the opener 2-1.
The Maple Leafs were without captain John Tavares after he sustained a concussion and knee injury on a scary collision 10 minutes into Game 1.
Toronto took its first lead of the series at 5:15 of the second period when Matthews — the NHL goals champion this season with 41 in 52 regular-season games — buried Justin Holl’s rebound on an odd-man rush to make it 2-1.