In related news, Canadiens goaltender Carey Price is one of the hottest in the NHL, with a .947 save percentage and 1.47 goals-against average in six starts since Claude Julien took over for Michel Therrien as coach Feb. 14.

BROSSARD, Quebec -- The Montreal Canadiens are one of the hottest teams in the Eastern Conference, with four straight wins heading into their game Saturday at the New York Rangers (7 p.m. ET; NHLN, CBC, TVA Sports, MSG), a potential first-round matchup in the Stanley Cup Playoffs.

"It's a big part of it," forward Brendan Gallagher said after practice Friday. "Every team relies on their best players to be their best players. He's our best player."

The link between Price's play and the Canadiens' recent run of success is impossible to deny, but there is more going on here than simply a hot goaltender leading his team to undeserved victories.

Video: NSH@MTL: Price kicks out pad to deny Smith in front

The Canadiens are also changing the way they play in front of Price under Julien, and as they get more accustomed to that, the victories should keep coming. At least in theory.

Price said he's noticed a change in how the players in front of him are adjusting to the new system but that the biggest change to the Canadiens has been between the ears.

"Attitude-wise, for sure," Price said. "I think that's the most important part. It was just not confident [before]. Any team that goes through a funk will tell you that it's just not a fun thing. Especially with the uncertainty too from the [NHL] Trade Deadline (on Wednesday). So you add all those things up, they were just kind of looming over the room.

"Now that those things are gone I feel like there's kind of a rejuvenation of energy."

Price's save percentage was at .917 at the time of the coaching change, 16th among NHL starters, dropping from a .940 mark and second in the NHL two months earlier on Dec. 16.

Price's percentage has climbed to .921, tied for ninth with Robin Lehner of the Buffalo Sabres entering play Friday. But he hasn't done it alone.

The changes instituted by Julien in the defensive zone as well as the arrival of defenseman Jordie Benn in a trade with the Dallas Stars on Monday have made Price's life significantly easier, setting off a chain reaction that could result in good things for the Canadiens.

Video: CBJ@MTL: Price makes OT stops on Johnson, Atkinson

With Price playing better and seeing fewer high-quality scoring chances, the Canadiens are free to work through their current offensive struggles while also remaining in games, and they've been winning them of late. The Canadiens have scored 10 goals over the four-game winning streak, with three of those goals coming in overtime, and two of those overtime goals coming on the power play.

Price has allowed three goals in his three starts over the streak, as many as backup Al Montoya allowed in a 4-3 come-from-behind overtime win at the New Jersey Devils on Monday.

"He's your last line of defense and to know he's on top of his game is always a good thing," defenseman Jeff Petry said. "Knowing you have the ability to make plays and if a mistake happens or a turnover happens, knowing that your goalie is on top of his game helps everyone's confidence in here."

Julien said that the main thing he has tried to institute in the defensive zone is to outnumber the opposition in puck battles along the walls and in the corners in order to retrieve the puck quickly and exit the zone. The Canadiens, he said, have adjusted well to those first two aspects but now have to work on exiting the zone cleanly out of those situations.

So the Canadiens remain a work in progress but have been allowed to be while winning because their goaltending has been so good, in part because of the changes Julien instituted.

Video: CBJ@MTL: Price makes big stops on Werenski and Saad

As an example, Price is seeing two fewer shots on goal per 60 minutes under Julien (27.8) than he was under Therrien (29.8).

"When I got here, things weren't going well," Julien said. "I'm not going to say they hit bottom, but the confidence was really low. It's pretty hard to turn things over quickly. You go step by step. I think defensively we've tightened up, which gives us a chance to win every night. Now we've won four in a row so guys are starting to feel better about themselves, so now we're attacking the offensive part of our game."

If the Canadiens find that offensive component of their game over the next month, not only would a spot in the playoffs become far more likely, the chances of going deep into the spring would increase dramatically.

In the meantime, Price is giving the Canadiens a chance to figure things out while they are winning, a luxury few teams have.

"Every team in the NHL that has success has a great goaltender," Julien said. "We're no different."