Alex Galchenyuk broke a tie with 3:29 left and Max Pacioretty added an empty-net goal to lift Montreal over New York 4-2 on Sunday night to complete a weekend home-and-home sweep.
The victory, however, was overshadowed by Gallagher's injury.
The 23-year-old left the game midway through the second period after blocking a slap shot by Johnny Boychuck. Gallagher tried to play through the pain but retreated to the dressing room and did not return.
Coach Michel Therrien confirmed Gallagher fractured two fingers on his left hand. He will undergo surgery on Monday and is out indefinitely.
"He's a guy that shows up every night," captain Pacioretty said of his linemate. "To see that happen, the way it happened, it shows the type of warrior he is. It's tough playing without him. We hope for the best. We need him."
Gallagher has not missed a game since Nov. 15, 2013 — a streak of 166 consecutive games.
"He's a big leader on this team," Galchenyuk said. "The way he plays, he contributes a lot. He blocks shots, he's a warrior out there. It's unfortunate to see him go down like that."
Galchenyuk one-timed a pass from P.K Subban for this third goal of the season during a power play. It was his first goal in 11 games and just his third of the season.
"It was one of the best feelings, especially when you haven't scored in a while," he said. "You try to stay positive and work hard. The last couple of games I worked on my game more and got more shots. I knew it was coming."
About 2 minutes later, the Islanders were called for too many men and Travis Hamonic was given a game misconduct penalty, setting up Pacioretty's power-play empty-netter.
David Desharnais also scored on the power play for his seventh goal and Tomas Fleischmann added his seventh this season for Montreal. Carey Price made 21 saves and the Canadiens followed a 5-3 win over the Islanders on Friday night with another victory.
John Tavares gave New York a 1-0 lead late in the first period, and Anders Lee made it 2-1 Islanders with 8:07 left in the third. Thomas Greiss made 23 saves.
Montreal has now defeated New York in six straight encounters and in nine of the last 10.
On the opening goal by Tavares, Price gave up an uncharacteristically juicy rebound on Hamonic's shot from the point. Winger Kyle Okposo jumped on the puck, circled Price and fed Tavares for an easy tap-in with 1:19 left.
Desharnais scored the equalizer on the power play at the 9:37 of the second. The Canadiens forward got the better of Hamonic during a goal-mouth scramble, connecting on a loose puck in the blue paint.
Fleischmann gave the home team the lead on a great individual play with 5:51 left in the second. With Montreal playing short-handed, Fleischmann stole the puck from Okposo at the blue line and fired home his seventh of the season on the breakaway.
The Canadiens now lead the NHL with five short-handed goals.
As time expired on a penalty to Dale Weise, Lee tied the game 2-2.
Recalled from the AHL's St. John's IceCaps, 22-year-old Sven Andrighetto made his season debut. The speedy forward finished the game with 10:23 of ice time.
NOTES: Pacioretty got his 300th career point. ... Montreal forwards Devante Smith-Pelly (lower body) and Torrey Mitchell (lower body) were not in the lineup. ... Price improved to 9-2-0 on the season. The Canadiens netminder is now 11-3-3 career against the Isles.