"Can I ask the first question? How high did Pacioretty jump on his hit? Can anyone tell me?" Rangers coach John Tortorella asked to open his postgame news conference. "I'm asking you guys. Over/under?"
When a reporter responded with a guess of six inches, Tortorella replied "You're wrong."
Girardi went down in the game's final minute when he blocked a hard shot from Montreal's P.K. Subban.
Tortorella acknowledged that injuries are part of the game and something his team has to deal with, but didn't use that as an excuse for the Rangers' struggles.
"We've just got to try to gain some confidence, stabilize ourselves when we lose a couple," he said. "Coming into the last three games here, we were playing pretty well. We can't get into a panic mode. We just need to get more minutes consistently out of our players."
Martin Biron, in his third start of the season, stopped 15 shots for New York (8-7-2), which has just one win in five games.
After a scoreless first period in which the teams combined for nine shots total, the action picked up in the second.
Cole hit the score sheet for the first time in 10 games when he netted his third goal of the season at 1:20. A point shot from Montreal defenseman Raphael Diaz went through Eller's skates and found Cole, who wristed a shot from the left circle inside the far post.
The Canadiens doubled the lead at 13:36 when Galchenyuk drove to the Rangers net and took a shot that deflected up off Girardi and landed in the net.
Quick puck movement on a late power play helped set up the Canadiens' third goal. Subban dished the puck from the point to Galchenyuk behind the goal line, and the rookie passed it to Eller, who scored at 19:34 from in the right circle.
NOTES: Canadiens winger Brendan Gallagher made his return to the lineup after missing three games because of a concussion. ... LW Rene Bourque missed the game with flu-like symptoms ... Forward Christian Thomas, son of former NHL player Steve Thomas, made his NHL debut for New York.