Mika Zibanejad had two goals and an assist, Alexis Lafreniere had a goal and an assist, and Igor Shesterkin made 26 saves for the Rangers (53-21-4), who have won three in a row and maintained their five-point lead on the Carolina Hurricanes for first place in the Metropolitan Division.
They lead the NHL with 110 points and four games remaining.
The Rangers can set their record for most wins in a season when they play the New York Islanders at UBS Arena on Tuesday. They won 53 games in the 2014-15 season.
"There's stuff on the line for us," Rangers captain Jacob Trouba said. "I think as athletes that's kind of what's engrained in your head, if there is something you can go out there and get you want to go out there and get it."
Cole Caufield extended his goal streak to four games and Cayden Primeau made 41 saves for the Canadiens (29-36-12), who have lost three in a row, including 4-2 to the Toronto Maple Leafs on Saturday.
"It's a tough building to come into, especially on a back-to-back after playing a good team last night as well," Primeau said. "I just tried to give the team the best opportunity. They're a good team. They're the best arguably right now."
Caufield scored at 19:30 of the first period to give the Canadiens a 1-0 lead. David Savard's shot from the point went wide and from behind the goal line Caufield got the puck and banked in it off Shesterkin.
New York got even 1-1 on Zibanejad's power-play goal at 12:31 of the second period.
He attempted a pass from the left face-off circle to Chris Kreider at the far post, but the puck hit off Joel Armia's right skate and redirected through Primeau's legs.
"To being going into a third period against them 1-1 it's good for us," Primeau said. "There's lots of good we can take."
But the Rangers took over in the third, scoring four times.
It started when Kreider gave them a 2-1 lead at 3:59 with a power-play goal off a netfront deflection of Panarin's wrist shot.