Caufield is looking to become the first Canadiens player to score 50 goals in a season since Stephane Richer in 1989-90.
Montreal, which is third in the Atlantic Division, blew a 2-0 lead midway through the third period but bounced back to win its seventh straight.
Alex Newhook also scored and Jacob Fowler made 21 saves for the Canadiens (44-21-10).
Adam Fox and Will Cuylle scored and Igor Shesterkin made 22 saves for the Rangers (31-36-9), who had a three-game win streak snapped. They were eliminated from playoff contention on March 25.
Caufield’s 49th goal of the season and second of the night gave Montreal the 3-2 lead with 5:05 left in regulation. He slid the puck past Shesterkin after winning it in the offensive zone.
He scored his 48th of the season at 6:20 of the second period to give Montreal a 2-0 lead. He took a pass from behind the net from Juraj Slafkovsky and fired a shot over Shesterkin’s right shoulder.
Caufield has 28 goals in his past 27 games. He is one goal behind Nathan MacKinnon of the Colorado Avalanche for the NHL lead.
His first goal came 1:44 after Newhook gave Montreal at 1-0 lead at 4:36 of the second with a one-timer on a feed from Ivan Demidov that beat Shesterkin over the blocker.
Fox cut the Canadiens’ lead to 2-1 at 9:23 of the third, collecting a loose puck to the right of the goal and putting it past Fowler, who was down on the ice.
The Rangers made it 2-2 at 14:08 when Cuylle went to the net and deflected in a shot from Jonny Brodzinski in the slot.
