Price leads the NHL with 36 wins. That equals Ken Dryden's Canadiens record through 50 games played, set in 1976-77 when Montreal went 60-8-12 to set the record for points in a season (132).
"Personally, I think a shutout is a team stat, it's not an individual stat," said Price, who is 14-1-1 with a 1.23 goals-against-average, .955 save percentage and four shutouts since Jan. 14. "We've been committed to playing defense all year and I think that number reflects that."
Price, who has 31 NHL shutouts, had six in 59 starts last season. His career high is eight in 2010-11, when he started 70 of his 72 games.
"He's been unbelievable for their team all year," Maple Leafs captain Dion Phaneuf said. "He's been extremely consistent. I think he's one of the top goalies in the League consistently year after year, and this year I would say he's probably the top goalie in the League. He's very well positioned, he fights through traffic very well.
"But the biggest thing for us is, I don't think we got enough traffic on him, because when you let him see the puck he's going to stop the puck. Tonight we just didn't generate enough screen shots, and when you get screen shots you get rebounds. But give credit to him, he played well."
The Canadiens lead the Eastern Conference with 87 points and are two behind the Nashville Predators atop the NHL standings.
Montreal's fifth straight win against the Maple Leafs, third this season, came in its only home game in a stretch of six of seven on the road.
Price has a Canadiens-record 10-game winning streak on the road with Montreal to begin a four-game trip Monday at the San Jose Sharks.
"We've got a big challenge ahead of us, heading out on that road trip," Montreal right wing Brendan Gallagher said. "It's not going to be easy, but we're leaving on a good note. We've been playing pretty good road hockey lately, so we're confident going anywhere, but we know this is going to be as tough a test as we're going to get, so I think we're excited for the challenge."
Jonathan Bernier made 19 saves for Toronto (25-32-5), which had a two-game winning streak end. The Maple Leafs have lost 15 in a row on the road; they were winless in 18 straight road games during the 1982-83 season.
"They only had 11 shots after two periods," Maple Leafs coach Peter Horachek said. "We turned over that first goal, they have an empty-net goal, the third goal was clearly goalie interference. We did it to ourselves on the turnover, but I thought there was some good compete there."
Montreal defensemen Andrei Markov and P.K Subban, each a plus-5 in the Canadiens' 5-2 win at the Columbus Blue Jackets on Thursday, assisted on Plekanec's goal, which put Montreal up 2-0 at 12:57 of the first period during a delayed penalty against Toronto.
Markov went plus-3 and is plus-10 in his past three games; Subban finished plus-2 and is plus-8 in his past three games.
"A lot of guys would take that for a season," Gallagher said. "When you're playing with those two guys, you know they're looking to obviously defend first, but they're so creative offensively that they're going to get you the puck. They're going to create chances and it's just what they do.
"I think they've developed a lot of chemistry over the years playing together. They understand each other well and they jump up in the rush and they make pretty good plays, and it's pretty easy being on the ice with those two."
Desharnais increased the Canadiens' lead to 3-0 with his 10th goal at 1:02 of the third period. It was his 200th NHL point; he got his 201st when he scored into an empty net with 2:33 left.
Linemates Max Pacioretty and Gallagher each assisted on Desharnais' goals.
Malhotra, who had two assists in his first 52 games with Montreal, scored 5:00 into the first period.
Canadiens right wing Dale Weise set up the goal with a pass back to the 34-year-old center, who shot past Bernier for his first goal since April 13, 2014 for the Carolina Hurricanes in a 6-5 win at the Philadelphia Flyers.
"[Weise] made an incredible play there," Malhotra said. "He had the opportunity himself; he sucked the [defense] to him and gave me a free walk down Broadway, so it was a great play by him, very unselfish hockey, and I think that's been kind of our trademark this year."
Montreal defenseman Sergei Gonchar returned to the lineup two weeks after he sustained an upper-body injury on a hit by former Maple Leafs forward David Clarkson during the Canadiens' 2-1 shootout win against Toronto on Feb. 14.