MONTREAL -- James Reimer kept the Montreal Canadiens off the scoreboard, and the Toronto Maple Leafs completely overpowered their longtime rivals Saturday night.
Reimer made 37 saves for his first shutout in more than a year, and Phil Kessel had a goal and two assists to lead Toronto to a 6-0 win.
Leo Komarov scored his first NHL goal 59 seconds in for Toronto, which swept a three-game road trip for its longest winning streak since last season.
James van Riemsdyk and Dion Phaneuf each had a goal and an assist, and Tyler Bozak and Korbinian Holzer also scored.
"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," Maple Leafs coach Randy Carlyle said. "We got the two-goal lead, and then you know they're going to push back."
It was Reimer's seventh career shutout and his first since Feb. 4, 2012, when he stopped 49 shots in a 5-0 victory over the Senators in Ottawa.
"I was just trying to go out there and get another win," Reimer said. "This has been a good road trip for us. We wanted to finish it off on a good note, and the team worked hard and we were able to do that."
Carey Price stopped 22 shots for Montreal, which has dropped three game in a row, including a 5-4 shootout loss in Buffalo on Thursday night.
"We had a really slow start," Canadiens coach Michel Therrien said. "They beat us with speed. They were ready to play and we weren't. We tried to make a push in the second period. It was just a bad night. We got shots, but we didn't have any net presence."
There were several fights in the third period, including an uneven matchup between 6-foot-5 Maple Leafs left winger Frazer McLaren and 6-1 Montreal defenseman Josh Gorges at 15:01.
"I give him credit," McLaren said. "He's been in the league awhile, and I'm not out there to hurt guys. He's a feisty guy, and he stood in there and wanted to go, but I don't want to hurt anyone."
That mismatch was precipitated by Toronto's Colton Orr taking a run at Canadiens center Tomas Plekanec, which saw 5-7 Montreal captain Brian Gionta come to his teammate's defense.
Canadiens forward Brandon Prust fought with Mark Fraser early in the third, and Prust picked up a double roughing minor and a 10-minute misconduct at 11:30 for his part in a wild scrum that saw Montreal's Max Pacioretty claim he was bitten by Maple Leafs center Mikhail Grabovski.
"What can you say," Gorges said. "That doesn't belong in our sport. It doesn't belong in hockey. If you get in there, stand up for yourself, be a man, drop your gloves. If you want to do that, you'll have respect. But bite somebody? That doesn't belong in our league."
Therrien expects both that incident and Orr's run at Plekanec to be reviewed by the league.
"I saw the bite. You can see that on the video," Therrien said.
Carlyle traced the bad blood back to one Montreal player he declined to name before answering a question about what part he felt Prust played in the game.
"Well, Prust, we know what kind of player he is, and he goes out and cheap-shots Grabovski," Carlyle said. "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 think coming. That's not happening to our group."
Komarov opened the scoring after 59 seconds on a setup by Nikolai Kulemin. Bozak made it 2-0 at 6:33 with his fourth goal, assisted by van Riemsdyk.
The Maple Leafs made it a 3-0 lead 3:36 into the second period on van Riemsdyk's team-leading seventh goal. Kessel, who assisted on van Riemsdyk's goal, increased the lead to 4-0 with a power-play goal at 18:01. Kessel scored for a second straight game after he was held without a goal through his first 11 games. He scored a career-high 37 goals last season and has led the Maple Leafs in goals in each of his first three seasons in Toronto.
Holzer scored his second goal of the season 4:20 into the third period. Kessel got his second assist on Phaneuf's first goal of the season, a power-play tally at 13:15.
"I think once we got up 4-0, it's one of those games where if they don't score soon, then it can get out of hand a little bit. It seemed like that's what happened," said Maple Leafs defenseman Mike Kostka, who fought with Canadiens rookie Brendan Gallagher. "I think that fourth goal was a bit of a dagger to put the nail in the coffin a little bit against them, and then they started getting a little chippy and they responded."
NOTES: The Maple Leafs play the Canadiens three more times this season, all at the Air Canada Centre, including the regular-season finale for both teams on April 27. ... Gallagher was given a minor penalty for diving 9:01 into the second period when he fell after he was spun around by Fraser, who was not penalized on the play. ... Canadiens right winger Ryan White was left out of the lineup. A fourth-line energy player, White has taken a number of costly penalties this season. His latest, a four-minute roughing double minor Thursday in Buffalo, helped allow the Sabres to erase a two-goal deficit in the third period.