"The crowd was electric," Price said. "They were behind us the whole way."
Maple Leafs defenseman Bryan McCabe broke his left hand when he was checked into the boards by Kostitsyn in the Canadiens zone on the play that led to Kovalev's goal at 8:32 of the third period that gave Montreal a 4-0 lead.
Toronto coach Paul Maurice was livid about Kostitsyn's role in the play. He said McCabe's hand was broken in three places, and the best-case scenario for the defenseman's return was six-to-eight weeks.
"It's not a natural thing," Maurice said. "It's not like getting hit into the boards where you can recover, but when you get hog-tied around the throat and you go back into the boards ... that's just brutal."
McCabe, who had played 21 minutes, 20 seconds when he got hurt, had averaged 26:33 through Toronto's 32 previous games. He had four goals and eight assists in 27 games.
"There aren't many 30-minute players around," said Tomas Kaberle, McCabe's defense partner.
Price, a 20-year-old rookie making his sixth straight start, came within 4:06 of recording his first career shutout.
"It's tough, but I'd rather get a win than anything else," Price said. "It's just another stat."
Boyd Devereaux scored for Toronto -- his fifth of the season -- 15:54 into the third period.
The Maple Leafs had won two straight, and six of seven.
Vesa Toskala stopped 21 shots a night after making 24 saves for his second shutout of the season in a 4-0 win Friday in Atlanta.
Koivu, who hadn't scored since Nov. 17, got the Canadiens going just short of midway through the first when he went behind the net and stopped suddenly before putting a sharp-angled backhand across the goal mouth to end a 12-game drought. The puck struck Maple Leafs defenseman Hal Gill's left skate and caromed past Toskala.
"I made a turn back in the corner and there were a lot of people in front of their goaltender, so I just wanted to get the puck in there, hoping for the best, and this time it went in," Koivu said.
Chris Higgins got his second straight assist as the captain made it 2-0 early in the second. Koivu took Higgins' centering pass off his right skate and cut past Toskala to score his second of the game.
"I just saw him sneaking behind the D there," Higgins said. "He fell behind the coverage. It was a nice play. I didn't really put it on his tape, but with the skills he has you just have to put it near him and he'll get it."
Kostitsyn made it 3-0 at 11:17 with his sixth goal, and Kovalev increased the lead to four goals with his 14th 8:32 into the third.
"I thought we really played well for 60 minutes -- tight, defensive hockey, which is going to make us successful," Koivu said. "We showed that when we play well defensively we're going to get some chances to score. Tonight the puck went in."
Canadiens winger Sergei Kostitsyn, Andrei's younger brother, assisted on Koivu's first-period goal for his first NHL point. Sergei Kostitsyn was recalled from Hamilton of the AHL on Thursday and made his big-league debut in the Canadiens' 4-1 win in Philadelphia.
Four fans behind the Maple Leafs bench were removed by security guards in the third period after a couple of drinks were poured over the glass -- Matt Stajan was doused by one drink. ... Canadiens G Cristobal Huet dressed as Price's backup after missing five games because of a groin injury. Huet posted Montreal's only shutout this season. ... The Canadiens returned G Jaroslav Halak to Hamilton of the AHL earlier Saturday.