Chris Kreider scored for the third straight game, Mika Zibanejad had two assists, and Igor Shesterkin made 31 saves for New York (1-1-1) in Gerard Gallant's first win as Rangers coach.
"The goaltending on both sides was excellent so it was definitely good to get that first win for our team," Gallant said.
Lafreniere, the No. 1 pick in the 2020 NHL Draft from nearby Saint-Eustache, Quebec, scored on a 2-on-1, deflecting a pass from Zibanejad to put the Rangers up 2-1 at 9:50.
"Obviously to score in Montreal, it's pretty fun," Lafreniere said. "The team played well. You know, a great effort, and obviously a nice pass by Mika on the goal. It's hard to imagine anything better. It was a really nice effort by the whole team."
The goal, with Lafreniere's family looking on from a suite, came 26 seconds after the Canadiens tied the game.
"He's still a really young kid but he's a talented kid, and we asked him to play a better two-way game and he's responded to that," Gallant said. "He created three or four chances tonight. He scored a nice goal, he had some other chances, so we really like the progress from training camp until right now."