Toffoli pushed the lead to 3-0 when he scored into an empty net at 17:22.
"This was huge for our whole team," Canadiens forward Phillip Danault said. "We know we can play against good players. Everyone did their job, that's how we won, and Price was solid every single night giving us a chance to win. A lot of pride here, a lot of pride in that dressing room and we definitely want more now."
William Nylander's one-timer through traffic cut it to 3-1 with 1:36 left.
"I don't think there's much to be said," said Maple Leafs forward Auston Matthews, who finished the series with one goal in seven games after leading the NHL with 41 in 52 regular-season games. "I'm not really sure how to sum it up. It's extremely frustrating all around."
Canadiens coach Dominique Ducharme said he felt coming into the game that Montreal was confident in its ability to complete the comeback with a series win.
"We played Game 5, Game 6 the same way," Ducharme said. "We had our backs to the wall, and for us tonight it was the same mindset, the same way to prepare. I felt our guys were in the right place and even more confident than before because we had just won those last two games. It was not that different of a day for us. I think our guys prepared really well and I think it showed on the ice."
NOTES: This was the second time the Maple Leafs and Canadiens faced each other in a Game 7. The first was Toronto's 3-1 victory in the 1964 Stanley Cup Semifinals. … The Maple Leafs were without defenseman Jake Muzzin, who sustained a lower-body injury in Game 6 and is expected to need at least three weeks to recover. … Marner, who was second on Toronto this season with 20 goals in 55 games, did not score in the series, playing seven games. … Perry scored for the fourth time in a Game 7 and played his ninth. He is third in Game 7 goals among active players, trailing Patrice Bergeron of the Boston Bruins (six goals in 12 games) and Paul Stastny of the Jets (five goals in six games).