Price made 36 saves as Montreal beat the Winnipeg Jets 3-0 on Tuesday. Canadiens captain Brian Gionta said the win only happened because of their goaltender.
"We had a great start, but the second and third (periods) we kind of laid back a little too much," said Gionta, who played his 700th career game after he missed the last game to attend to family matters in Montreal.
"They adjusted to us and kind of took it to us and we relied on Carey the last two periods, and Carey basically won that game for us."
Brandon Prust, P.K. Subban and Daniel Briere, with an empty-netter on the power play, scored for Montreal (4-2-0), which extended its winning streak to three games and ended a four-game road trip.
"The last couple games, (Price has) been our best player," winger Rene Bourque said. "We need him to do that. It's great to see."
The victory marked Price's 20th career shutout.
"I'm not going to take all the credit for our wins," said Price.
"We've had a lot of sacrifices along the way. Different guys step up to the plate at different times, at different points during each of these four games.
"We definitely put out a great effort tonight."
Ondrej Pavelec faced 25 shots for the Jets (3-4-0), who were playing their third game of a six-game homestand. They host St. Louis on Friday.
With a number of fans wearing Habs jerseys in the stands at MTS Centre, the visitors quickly opened the scoring.
A Briere shot off the boards led to Prust's goal, as the puck bounced to him at the corner of the net and he poked it in behind Pavelec to make it 1-0 at 2:06.
It took the Jets just under seven minutes to get their first shot on goal, a span that included their own power play, as the Habs kept most of the action in Winnipeg's end.
"We couldn't generate a whole lot," Winnipeg coach Claude Noel said.
"We got some shots on net, they blocked a lot of shots. We didn't get enough through. We didn't get enough traffic and we struggled."
Winnipeg killed off a penalty, but about a minute later Subban blasted a one-timer past Pavelec at 11:28, his eighth point in six games. The shots on goal at that point were 7-1 for Montreal.
The Jets finally turned it on during another power play, boosting their shots on goal to close Montreal's advantage to 10-8 at the end of the first period.
Canadiens forward Max Pacioretty fell to the ice during the first period after getting tangled between a couple of Jets players on the way to the net. He didn't' put any weight on his left leg as he was helped off the ice and didn't return.
The Jets kept pace with the Habs in the scoreless second period and took the lead in shots on goal 21-19, but Noel said the numbers can be deceiving.
"When you look at the scoring chances for our team, (Price) saw a lot of pucks," he said.
"He was able to get it stopped quickly, just clear shots to the net. So either we're not getting there or we're not getting shots through."
Despite quickly starting the third period shorthanded, Winnipeg had some early scoring chances, including two by captain Andrew Ladd, although on one he bobbled the puck.
Noel kept the same lines he did in Sunday's 3-0 win over New Jersey, which saw Ladd move from the top line to the second one with rookie centre rookie Mark Scheifele and Michael Frolik.
Evander Kane was on the top line with centre Bryan Little and right-winger Blake Wheeler, whom Noel said is trying, but not playing very well.
Winnipeg went on the power play with seven minutes left in the game after Briere was called for hooking, but Price made one save and Ryan White blocked the other shot.
With Pavelec pulled and the Jets shorthanded because of a Little cross-checking penalty, Briere scored his first of the season at 18:42.
"It's unfortunate that it takes two goals to get a little desperation in our game," Jets captain Andrew Ladd said.
"You've got a find a way to get going right off the hop. I mean there's enough energy in this building to do that and to start the game with the right intentions."
Notes — The Canadiens return to Montreal for a five-game homestand. ... Habs defenceman Josh Gorges played in his 500th game and assisted on Subban's goal.