The Eastern Conference-leading Rangers have won four straight and have 107 points, one better than the Western Conference leaders St. Louis Blues with four games remaining.
"That's not something that we're ultimately focusing on, it's more our game," Rangers captain Ryan Callahan told reporters.
"The last couple games here, you could feel it starting to come again. We're starting to get that confidence back, which is really important as you head into the postseason."
Rangers defenseman Michael Del Zotto scored two third period goals and had an assist to lead the offense.
"The thing is, we're moving the puck quickly. We're not holding onto it too long," said Del Zotto.
"Right now, the puck's moving so quickly, and no genius has to tell you that the puck moves more quickly than a body, so when we're doing that with the skill we have, we're able to score goals."
Brad Richards scored a second period goal and had two assists, while Marian Gaborik opened the scoring for New York in the first period by settling a loose puck in front of the Montreal goal before snapping a shot past Carey Price.
"It's an awfully good team that we're trying to outwork, and I thought we outworked them and had some zone time," said Canadiens coach Randy Cunneyworth.
"The next dilemma is getting the puck to the net. The couple times that we did, we were effective, but their goaltender played well."
Rene Bourque denied Rangers goalie Henrik Lundqvist a shutout by scoring on Montreal's final shot of the game with less than three minutes left to play. Lundqvist made 19 saves for his 38th win.