Eller was a healthy scratch in the Canadiens' second and third games this season, but the 23-year-old Dane has found a home in the lineup since he has gotten in.
While he hasn't gotten onto the score sheet night after night, he is doing the right things on the ice.
"At some point in your career you have to define what kind of player you're going to be and make some decisions," he said. "I feel that's where I'm at in my career right now."
After bouncing around the lineup in his first two seasons and spending a good part of the first month of this season centering the fourth line, Eller has more recently been paired with Galchenyuk, with different wingers joining them.
"I've seen him play for a couple of years. He's got talent and can play both ends of the ice," Canadiens coach Michel Therrien said. "It's often a matter of confidence. His work ethic is exemplary right now. He's getting involved, he's moving his feet, getting on the puck and creating turnovers. It's paying off for him."
Talking things through with Therrien has helped, Eller said, as has speaking with the team's sports psychologist.
"But in the end, it has to come from the player himself," he said. "You can get the guidelines and be pointed in the right direction, but in the end you have to do the work yourself."
Carey Price made 17 saves for his second shutout of the season and held the Rangers to one total goal in two meetings this week. It marked the fourth time in Montreal's last five games that the opposition has been held below 20 shots.
"We addressed it tonight in our meeting before the game. We have a style to play," said Therrien, whose team is two points ahead of Pittsburgh for first place in the Eastern Conference. "It's a demanding style, but we want to be a team that's tough to play against. The guys did a great job again.
"We picked up seven points out of eight (this week). That's pretty exceptional."
The game was particularly costly to the Rangers, who have lost three straight (0-2-1) without injured star forward Rick Nash in the lineup.
New York was also missing forwards Darroll Powe and Arron Asham, and defenseman Michael Del Zotto. The Rangers then lost their top defensive pair -- Dan Girardi and Ryan McDonagh -- during the loss to the Canadiens.
McDonagh left in the second period after being boarded by Canadiens forward Max Pacioretty, and Girardi had to be helped off the ice in the third because of an ankle injury.
"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.
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.