The 24-year-old Eller has three goals and two assists in Montreal's opening two games. Gallagher has two goals, and Galchenyuk has four assists.
"I got off on the right foot," Eller said. "The whole line has been playing great. We're creating space for each other. If you create chances, the goals are going to come."
Gallagher picked up his second goal of the season and Brian Gionta and linemate Rene Bourque added goals for Montreal. Eller's line produced all three goals in a season-opening 4-3 loss to Toronto on Tuesday night.
Vincent Lecavalier, the Montreal native who was booed each time he touched the puck, scored for Philadelphia, coming off a loss to Toronto on Wednesday night.
Many in the Bell Centre crowd of 21,273 were on Lecavalier's case because he passed up Montreal to sign as a free agent with the Flyers this summer. The booing didn't seem to faze him.
"I just wanted to help my team win the game," Lecavalier said. "It's always special playing in Montreal and it was the same thing tonight."
Gallagher and Galchenyuk each coming off impressive rookie seasons. The team's top line is struggling with winger Max Pacioretty out with a wrist injury. Now the youngsters are getting more ice time, especially on the power play, than they got last season.
"That's our strength -- the depth of our scoring," said Gionta, who added that Eller is "a young kid who has grown. You can see how he's matured as a player."
Special teams were the big factor in a game dotted with minor penalties. Montreal went 2 for 9 with the man advantage and the Flyers were 1 for 5.
"It's tough to score when you're in the box," Flyers forward Max Talbot said. "You have to look at discipline. We'd start getting momentum and then we'd have to kill two minutes, so we have to clean that up."
Montreal had a 34-23 shot advantage.
Philadelphia hasn't scored an even-strength goal in its first two games.
Tomas Plekanec won a faceoff in the Flyers' zone and Bourque slipped a pass across the crease for Gionta to bang past Ray Emery for the opening goal 8:10 into the game.
The Flyers were victims of a quick whistle when Price lost a puck at his feet and Matt Read knocked it in, but it was ruled no goal. Philadelphia coach Peter Laviolette said it was not a major factor in the game because the score was still only 1-0 going into the third period and the Flyers still had a chance to win.
"After they scored at the start of the third, we lost our composure a bit," he said. "We're not going to win a lot of hockey games if we go to the box as much as we did tonight."
Eller backhanded in the rebound of a Gallagher shot that missed the net only 12 seconds into the third frame.
P.K. Subban's shot looked to have gone in during a third-period 5-on-3 but video review found it went in the side netting. Only 18 seconds after play resumed, Subban faked a shot and passed to Galchenyuk, who slipped it to Gallagher for a 3-0 lead.
Lecavalier was at the side of the net to lift the rebound of Mark Streit point shot past Price on a power play 9:13 into the third. Bourque added a power-play goal in the final minute.