Montreal then pulled out the win in the third period.
Galchenyuk finished off a play that began with an odd-man rush. Rangers captain Ryan Callahan got back and had a chance to break it up, but couldn't. Lars Eller moved the puck down to former Rangers forward Brandon Prust near the right post, and Prust quickly got it in front to Galchenyuk, who lifted a rising shot that caromed in off the crossbar.
"Throughout the game we kept telling ourselves to be patient with it, get pucks in deep," Callahan said. "We tried to focus on not turning the puck over. Unfortunately in the third, we turn one over, got a 3-on-1 against us, and it ends up being the winner."
The Canadiens got even with 1:15 left in the second when Josh Gorges carried the puck in the Rangers end along the left-wing boards and flung a pass to the middle. Pacioretty ripped a drive from the high slot that beat Lundqvist inside the right post.
Pacioretty, who missed four games from Jan. 27-Feb. 2 because of appendicitis, scored for the second straight night. He has two goals and three assists in three games.
Stralman had given New York the lead with his second of the season, scored with 7:31 left in the second. During a delayed penalty, Derek Stepan made a pass from the left side to Stralman at the right post. The defenseman's first shot was stopped by Price's pad, but Stralman then knocked the rebound past him.
Neither the Rangers nor Canadiens showed a whole lot of drive in an uneventful first period that featured no goals, one penalty and a total of eight shots — including five by New York. Montreal didn't record its first shot of the game until only 3:49 remained in the first, when Prust pushed the puck in on Lundqvist from in-close.
"I was definitely amped up for this," said Prust, who played parts of three seasons with New York before leaving this past offseason. "Ranger fans were happy with my time here. I respect them. I heard a few cheers."
NOTES: Stralman has his two goals in a four-game span. ... Montreal has allowed five shots in the first period in each of its past three games. ... Carl Hagelin earned an assist for New York, but his four-game goal streak was snapped. ... Montreal was whistled for two penalties. The Rangers were called for one. ... Brandon Mashinter and Chris Kreider were in the New York lineup for Nash and Darroll Powe (concussion).