Montreal had 18 shots and made the most of very little offense against Henrik Lundqvist.
The Canadiens tied it late in the second period on Max Pacioretty’s goal.
Montreal went ahead for good when Galchenyuk matched Pacioretty with his second of the season 1:48 into the third.
SHARKS 2, BLUES 1
In St. Louis, Antti Niemi made 25 saves and Tim Kennedy scored in the third period to help San Jose end a seven-game winless streak.
The Sharks’ seven-game skid was their longest streak since a 10-game run Nov. 5-30, 2005.
Joe Thornton also scored for San Jose.
PREDATORS 4, RED WINGS 3 (OT)
In Nashville, Tenn., Shea Weber scored 44 seconds into overtime to give the Predators a victory against Detroit.
Craig Smith, Gabriel Bourque and Roman Josi also scored for Nashville, which had lost its past two games.
SENATORS 3, ISLANDERS 1
In Ottawa, Andre Benoit and Dave Dziurzynski scored their first NHL goals and Craig Anderson made 37 saves and the Senators defeated the New York Islanders.
Colin Greening also scored for Ottawa.
Travis Hamonic scored for the Islanders, who got 23 saves from Rick DiPietro in his third start of the season.
JETS 2, SABRES 1
In Buffalo, N.Y., Ondrej Pavelec made 29 saves to help Winnipeg snap a three-game skid.
Andrew Ladd’s goal that made it 2-0 early in the second period stood up as the winner, and Bryan Little also scored for Winnipeg.
The Jets won for the third time in 10 games while opening a season-high five-game road swing.
LIGHTNING 4, MAPLE LEAFS 2
In Tampa, Fla., Steven Stamkos scored his 10th goal, Benoit Pouliot had three assists and the Lightning beat Toronto.
Vincent Lecavalier, Alexander Killorn and Matthew Carle also scored for the Lightning, who have won two in a row after an 0-5-1 skid.