He was right.
One of the fights led to a scary moment when Montreal's new enforcer George Parros was carried off on a stretcher in the third period after he fell on his face during his second bout of the night with Colton Orr. Parros sustained a concussion and went to hospital for further evaluation.
Between the five fights in the game, Reimer won his fourth straight start against Montreal.
"That was the hunch," Carlyle said. "He's played very well in this building in the time I've been here. I felt he gave us the best chance to win."
Reimer got the nod over Jonathan Bernier, who joined the Maple Leafs from the Los Angeles Kings in the offseason. Reimer proved his coach right, even if he doesn't acknowledge the debate regarding who should Toronto's starting goalie.
"When I'm in there, I'm not competing against anybody on my team," Reimer said. "That's not what it's about.
"I'm competing against the other team, not the guys sitting beside me. They gave me the nod and I wanted to make the most of it and play my hardest for my teammates. Luckily enough, we won."
Tyler Bozak scored a short-handed goal at 17:19 of the second period, and Raymond netted the winner 5:10 into the third before Lars Eller's second of the night closed the gap to one goal with 2:22 left.
The Canadiens pushed hard in the closing minutes, but couldn't score the tying goal.
"The execution by our team was not there," Montreal coach Michel Therrien said. "A lack of execution with the puck led to two goals, and a lack of focus without the puck cost the other two."
Eller's three-point night included an assist on Brendan Gallagher's goal for Montreal, which will also face Philadelphia next at home on Saturday night.
The Canadiens' 350th consecutive sellout crowd was electric as usual for a Montreal-Toronto game, and it didn't lack for action.
But the mood turned somber 2:34 into the third period when Parros was prone on the ice. Orr had fallen and pulled down Parros, who was bleeding and looked woozy. A team of trainers from both teams spent several minutes treating him.
"Give credit to our training staff, our medical staff," Canadiens defenseman Josh Gorges said. "The doctors were out there in five seconds. They didn't waste any time. I just hope he's all right."
The crowd chanted Parros' name as he was wheeled off the ice.
Carlyle credited his team's special teams for the win. The unit produced the short-handed goal from Bozak and opened the scoring on a power play.
"I thought out special teams were the difference in the game," he said. "The short-handed goal turned everything in our favor, and the power play got us going.
"But I liked that when we got up 4-2 we were able to play more of the grind game in the offensive zone and chew the clock up."
The Maple Leafs were on a two-man advantage when van Riemsdyk partially fanned on a shot at the side of the net, and the puck slipped between Carey Price's pads 8:01 into the game.
The teams were each down a man when Raphael Diaz sent a pass to Eller for a goal at 10:08. Toronto was caught on a 3-on-1 when Montreal got the puck behind Carl Gunnarsson, and Eller fed Gallagher at 13:54.
Phaneuf tied it 8:36 into the second as he broke in on the left side to put a wrist shot inside the far post. It was the 19,000th goal in Leafs history in 6,169 games since 1917.
Bozak put Toronto ahead when he poked the puck away from defenseman Andrei Markov at the point and went in on a break to beat Price to the stick side.
Raymond, playing his first regular-season game for Toronto, finished a give-and-go with Troy Bodie.
Montreal got a scare midway through the first period when Max Pacioretty left with an apparent wrist injury after a hit from Orr. He returned in the second period.
It is the fifth consecutive season that Montreal and Toronto played each other in an opener. Toronto leads 4-1, winning the last four. ... The Canadiens called up defenseman Nathan Beaulieu as insurance with Douglas Murray, Davis Drewiske and Alexei Emelin all injured. ... C Nazem Kadri played his 100th game for Toronto. ... Morgan Rielly was scratched by the Maple Leafs. Montreal sat out Beaulieu, Michael Bournival and Ryan White.