Nico Daws made 22 saves in his third straight start for the Devils (22-17-3), who have lost two in a row and are 1-3-1 in their past five games.
"We had a little breakdown on the last goal ... all we had to do was box out," New Jersey coach Lindy Ruff said. "Our goalie made the save (on the initial shot by Monahan). We just have to box out. It stings and stings even worse when there's five minutes left."
Timo Meier had an assist and four shots on goal in 20:41 of ice time in his return after missing six games with a mid-body injury sustained Dec. 30.
"It's frustrating, but what can you do?" Meier said. "You just got to keep going and stick with it, and if you do that it's going to come. We battled back and we shot ourselves in the foot by allowing a goal with about five minutes left."
Slafkovsky gave Montreal a 1-0 lead at 12:48 of the first period after scoring on a shot from the slot. Caufield had the primary assist on a waist-high slap-pass. The goal came 30 seconds after Montembeault denied Meier on a wrist shot in front of the net.
"It's pretty nice to play with [Caufield]," said Slafkovsky, who scored for a second straight game. "He's a special player and he can make plays like these. I'm just happy that I was in the right spot at the right time. It was kind of bouncing and I whacked it in."