''Me and Gallagher have played quite a bit together,'' said Galchenyuk, who was drafted third overall in 2012, behind former junior teammate turned Edmonton Oilers first overall selection Nail Yakupov.
''I love playing with (Gallagher). He is a fun player. If I give him the puck he usually makes no mistake with it. He's fast and has great vision.''
It was a special night for Gallagher who made his first pro appearance playing in his hometown of Edmonton.
''It was pretty cool,'' the 21-year-old said. ''I was pretty excited to come in here tonight and play in front of a lot of friends and family that I grew up with. I saw a lot of games in this building as a kid so it was really special walking down that tunnel tonight.
''I just wanted to help and contribute. To contribute by being on the score sheet is always fun.''
Brandon Prust and Max Pacioretty also scored and P.K. Subban had three assists for the Canadiens (2-2-0), who were making their second stop on a four-game Western Canadian trip.
''I thought it was a great team effort tonight,'' Subban said. ''We stuck to the game plan and we didn't get frustrated when they got a goal early on. We battled back and we did it for each other.
''It feels great to get our first win on this road trip. We have two more really important games and an opportunity to build some momentum coming out of this road trip.''
Ryan Smyth scored for the Oilers (1-3-0), who start on a lengthy six-game road trip.
Oilers coach Dallas Eakins said his team played well, but didn't have much puck luck.
''I wouldn't mind a break to go our way, he said. ''I thought we played a good game, probably the most solid game that we've played so far. Improvement is nice, but it's not good enough if you end up losing the game.''
There was no scoring in the first period, but there were some quality chances.
Edmonton's best early opportunity came 11 minutes in when defenseman Justin Schultz pinched in from the point and had a point-blank shot on net, but hit Montreal goalie Peter Budaj in the face, ripping off his mask.
With seven minutes left in the first, the puck was in the Edmonton crease with Oilers starter Devan Dubnyk out of the play, but defender Nick Schultz was able to swoop in and send it to safety.
The best chance for either team belonged to the Canadiens just a minute later as Rene Bourque clanged a shot off the post.
''It was a matter of missed opportunities in the first,'' Oilers captain Andrew Ference said. ''We showed a lot of jump right off the bat and we got a couple of power plays that I don't think we even got a shot on. We had some really good shifts and some really good portions of hockey and it was just taking our foot off the pedal.''
The Oilers went up 1-0 on the power play 2 1/2 minutes into the second period as Taylor Hall sent a pass in front from the side of the net and a diving Smyth was able to get a piece of it and direct it past Budaj.
The Canadiens tied the game with a power-play goal at 9:24 as Galchenyuk floated a pass to Gallagher at the side of the net and he was able to swat it in with the heel of his stick for his third of the season. Galchenyuk earned his sixth assist in four games on the play.
Montreal then edged ahead 2-1 with eight minutes to play in the second as Dubnyk was able to make a kick save in tight, but couldn't keep Prust from sweeping in his own rebound from the shot.
The Canadiens came close to adding to their lead with 11 minutes left, but Gallagher rang a shot off the post.
Montreal did make it 3-1 three minutes later, breaking out on a 2-on-1 with an Oilers defender pinching, as Gallagher made a good pass to Galchenyuk and he deposited his first of the season before Dubnyk could get across.
The Oilers pulled their goalie with four minutes left and had a chance when Ales Hemsky hit a post, but Pacioretty ended any hopes of a comeback with an empty-netter.
Notes: It was the first meeting between the teams since March 8, 2012, a game won 5-3 by the Canadiens. ... Peter Budaj made his first start of the season in net for the Habs. ... Montreal defenseman Josh Gorges was able to return to the lineup after only playing one shift in the third period in his team's loss to Calgary on Wednesday night before leaving with an injury. ... Smyth returned to the ice for the Oilers after being a healthy scratch in Edmonton's last game.
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