Price was crucial to the win while the Canadiens put only four shots on goal through the first half of the game, turning away a number of Sharks shots to maintain a 1-1 tie while his teammates generated nothing offensively until Plekanec scored the go-ahead goal at 13:58 of the second.
He made 25 saves, and allowed one goal or fewer for the eighth time in his last 12 starts.
But by and large, the Canadiens limited the Sharks to perimeter shots, the ones Price generally stops in his sleep.
"Our guys did a really good job shutting down their top guys," Price said. "They're a talented team over there and they're hard-working too. We stepped up to the plate."
"We had a lot of shots -- some were quality chances, some were from the outside," Heatley said. "But if you let Carey see pucks he's going to stop them. He had a lot of shots, but he had a lot of easy saves tonight."
Just like his goalie does, Spacek tried to shift the credit for his defensive performance.
"We got great help from the forwards," he said. "Sometimes we gave up those shots from the wide side, but Carey's ready for that. We had to cover the slot and the rebounds, and I think we did a pretty good job."
Canadiens coach Jacques Martin has grown accustomed to leaning on Hamrlik and Spacek to compensate for the loss of star defenseman Andrei Markov, who will undergo reconstructive surgery on his right knee Wednesday and miss the rest of the season.
In Martin's 109 regular season games behind the Canadiens bench, Markov has only played in 52 of them.
"We're counting on those two to be our shutdown pair," Martin said. "They did that last year for more than half the season in the absence of Markov, and since Markov's gone for the rest of the year, those two will face the opposition's top line most nights."
Mathieu Darche and Mike Cammalleri also scored for the Canadiens (17-8-2), who snapped a 10-game run of alternating wins and losses to string together two in a row for the first time since Nov. 16.
"We wanted to try and get on a bit of a roll, it's been up and down," Price said. "So getting two in a row is nice."
Benn Ferriero scored the lone goal for the Sharks (12-9-4), who have a seven-game run of their own where they've followed a win with a loss.
Not only did Hamrlik and Spacek shut down the Thornton line defensively, Hamrlik even got the better of Thornton as he fended him off on a partial breakaway at 8:22 of the third to get a weak backhand off. Antti Niemi stopped the shot, but left a juicy rebound for Cammalleri to bury to make it 3-1.
Niemi made only 16 saves in the game as Montreal rarely threatened, but converted when it got an opportunity.
The Canadiens continued getting strong play from the line of Darche, Lars Eller and Benoit Pouliot, but the struggles of Scott Gomez continued. Though he had scored in consecutive games to run his season totals to 4 goals and 5 assists, Martin demoted him to fourth-line duty between Tom Pyatt and Maxim Lapierre midway through the game.
"There wasn't a whole lot going on with our other three lines, so I sent Gomez in there with Pyatt and Lapierre and I think it created some energy," Martin said, refusing to call the move a demotion. "I wanted to try and change the momentum of the game."
The Canadiens opened the scoring on a play that turned when a Sharks dump-in struck referee Ian Walsh in the Montreal end. Hal Gill picked up the loose puck, hit Pouliot in the neutral zone and he set up Darche at 6:00 of the first.
The Sharks tied it up when a seemingly harmless shot from a sharp angle by Ferriero appeared to catch Price off guard, beating him short side at 13:04 of the first.
1 - 0 MTL
1 - 1 Tie
2 - 1 MTL
3 - 1 MTL