Tyler Bozak scored later in the first period, James van Riemsdyk and Phil Kessel added second period goals and Korbinian Holzer and Dion Phaneuf, with his first of the season, scored in the third for Toronto (7-5-0).
The Leafs completed a sweep of a three-game road trip and are 6-1-0 away from the Air Canada Centre this season, including a 2-1 victory in Montreal in their season opener Jan. 19 with Ben Scrivens in goal.
Toronto jumped past Montreal (6-4-1) in Northeast Division standings. The Canadiens are 0-2-1 in their last three.
Reimer was a rock in goal, especially the second frame when Montreal had a 2-7 edge in shots. He made a deft glove save on an Erik Cole one-timer and thwarted Brian Gionta on back-to-back chances in his seventh career shutout.
Montreal outshot Toronto 37-27 overall.
The game wasn't a minute old when Nikolai Kulemin tipped the puck past Andrei Markov at the blue-line and the Montreal defenceman — coming off two knee surgeries — was unable to get back as Kamorov went to the net to tip in the pass on a 2-on-1.
It was the first-year winger from Estonia's first goal in 12 NHL games.
The goal seemed to throw Montreal into disarray, and the Leafs capitalized as van Riemsdyk banked a puck off Carey Price to an unguarded Bozak for a shot into an open side at 6:33.
Kessel put a move on the Montreal defence at the side of the net and fed the onrushing van Riemsdyk for his seventh goal 3:36 into the second frame.
Kessel got his second of the season and second in as many games on a power play as he picked the top corner from 15 feet out at 18:01.
After Holzer made it 5-0 four minutes into the fight-filled third period before Phaneuf scored from the slot at 13:15 while on a two-man advantage.
Price let in all six goals and finished with 21 saves.
Notes: Komarov was moved onto a line with Mikhail Grabovski and Kulemin. . . Ryan White was a healthy scratch a game after taking a costly penalty in Thursday's 5-4 shootout loss in Buffalo. Yannick Weber and Tomas Kaberle were also out for Montreal. . . Mike Komisarek was scratched for a fourth straight game for the Leafs and Dave Steckel didn't dress for a second game.