The third period was filled with fights, and there was an accusation by Montreal's Max Pacioretty that Mikhail Grabovski bit him and more venom over Colton Orr's apparent attempt to knee the Canadiens' Tomas Plekanec.
There was also a 37-save shutout by James Reimer, and Leo Komarov's first NHL goal only 59 seconds into the one-sided contest that started the rout.
"We had a really great start to the hockey game," said Toronto coach Randy Carlyle, whose club completed a sweep of a three-game road trip and is now 6-1-0 away from the Air Canada Centre, including a season-opening 2-1 win in Montreal on Jan. 19 with Ben Scrivens in goal.
"We did a lot of things in the first 10 minutes that kind of set the tone for our group for the rest of the night. We got the two-goal lead and then you know they're going to push back."
The Canadiens answered with 20 shots in the second period, but couldn't beat Reimer, who got his first shutout of the season and seventh of his career. Most of Montreal's shots were from far out, but he made sharp saves on an Erik Cole one-timer and Brian Gionta shot from in close in back-to-back plays.
"This has been a good road trip for us," said Reimer. "We wanted to finish it off on a good note and the team worked hard and we were able to do that."
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), which jumped past Montreal (6-4-1) in the Northeast Division standings.
"We weren't ready to start," said Montreal defenceman Josh Gorges. "Toronto, at home, in our building, and we're not ready to play? That's not good enough."
It got nasty in the third period, which started with a bout between Mark Fraser and Montreal's Brandon Prust at 1:09 and went further downhill after Holzer made it 5-0 at 4:20.
First, rookie Brendan Gallagher took on Michael Kostka and, a few minutes later, Prust was handed four minutes for roughing Toronto's Grabovski.
It was Pacioretty who emerged from the ensuing melee showing his wrist to the officials, claiming that Grabovski bit him. Both players were given 10-minute misconducts.
"That doesn't belong in our sport," said Gorges. "If you get in there, stand up for yourself, be a man, drop your gloves, and you'll have respect. But bite somebody? That doesn't belong in our league."
"I saw the bite," said Montreal coach Michel Therrien. "You can see that on the video. I'm sure the league's going to pay attention to that."
Neither Pacioretty nor Grabovski was made available to the media after the game.
After Phaneuf scored during a two-man advantage at 13:15, another donnybrook broke out when Orr clipped Plekanec's leg, although the Canadiens centre avoided a direct hit with a last-moment leap and was not injured.
Gionta and Rene Bourque jumped in, but it was Gorges who ended up fighting the six-foot-five Frazer McLaren, who was smiling as he held off the enraged Canadiens defenceman.
Therrien said the NHL's disciplinarians should look at that incident as well, but Carlyle pinned all the nastiness on Prust.
"We've got to take care of our own selves and we've got to look after business," he said. "And all the complaining that they want to do about it, the whole thing was started by what we felt was one player.
"Well, Prust, we know what kind of player he is and he goes out and cheap shots Grabovski. Well, what are we supposed to do? We're not supposed to play the rest of our players for the rest of the night? Well, they've got another thing coming. That's not happening to our group."
The blowout win and the battles that followed could make for lively meetings in the two clubs' next three meetings, which are all in Toronto Feb. 27, April 13 and April 27.
The Canadiens are 0-2-1 in their last three games and head south this week for games in Florida and Tampa Bay.
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.
Holzer made it 5-0 four minutes into the fight-filled third period before Phaneuf scored from the slot at 13:15.
Price let in all six goals and finished with 22 saves.
"They beat us with speed," said Therrien. "They were ready to play and we weren't. We got shots, but we didn't have any net presence."
Notes _ Komarov was moved up to a line with 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.