Pierre-Marc Bouchard and Brock Nelson had the goals for the Islanders, who ended a four-game road trip without a point. Montreal had a 31-26 advantage in shots.
The Islanders played their second game in less than 24 hours and were without recently acquired forward Thomas Vanek, who sustained an upper-body injury in a 5-2 loss Saturday night in Columbus.
"Everyone finds a way to do what they have to do at this level," said Nelson, who sat out the Columbus game. "I think everyone did a good job. We had good energy from the start, so I don't think it was a factor."
The Eller-Galchenyuk-Gallagher unit had a combined 19 points through Montreal's first five games of the season. But points have been harder to come by of late as the entire team struggled to put the puck in the net. The squad had only seven goals in the four previous games.
Everything clicked against the struggling Islanders, though.
"For some reason we just have that chemistry," said Eller, who has been briefly moved to other lines at times recently to try to shake up the attack. "Things just come naturally.
"Everybody's playing on their instincts, so there's not too much hesitation."
It started with the opening goal 1:46 into the second period when Galchenyuk sent Gallagher in on the right side for a wrist shot that beat backup goalie Kevin Poulin, who started in place of Evgeni Nabokov.
Eller's turn came at 16:34 on a power play when he one-timed Galchenyuk's cross-ice pass inside the far post from the right circle.
Galchenyuk got his goal at 10:37 of the third as he completed a tic-tac-toe play with his linemates, tipping the puck in from the edge of the crease after Gallagher caused a turnover in the New York zone.
The line combined for 10 of Montreal's 31 shots.
"They did a lot of a good things as well as contributing on offense," Therrien said. "I like how they pressured the puck carrier and created a lot of turnovers."
New York's penalty-killing woes on the road trip continued as Montreal went 2 for 5 with the man advantage. The Isles killed off only nine of 17 penalties in the four games.
The good news was their power play scored twice, ending an 0-for-22 drought spanning the previous seven games.
Bouchard beat Price with a shot from the top of the left circle to tie it 1-all at 7:23 of the second.
John Tavares' pass from behind the net went in off Nelson's skate 4:10 into the third. The goal was upheld after a video review.
"I knew I got a little piece of my stick on it and I felt it hit my foot, but I knew I didn't kick it in any way," Nelson said of his second career goal. "It was kind of a lucky bounce."
Montreal forward Travis Moen left after the first period with the flu. ... Forward Gabriel Dumont was called up from Hamilton of the AHL and George Parros sat out. ... IIHF President Rene Fasel was in attendance, as was former Soviet goaltending great Vladislav Tretiak, who was applauded by the Bell Centre crowd. ... Hard times for struggling Canadiens center David Desharnais: Even new Montreal Mayor Denis Coderre tweeted that Desharnais should be given a one-way ticket to Hamilton.
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