Galchenyuk stepped around Tyson Barrie just after a power play ended and whipped a shot past Reto Berra 3:28 into the extra period to give the Canadiens a 3-2 victory the Colorado Avalanche on Thursday night.
"Christian Thomas was cutting to the middle of the blue-line and I was calling for it he made a nice play to drop it to me," Galchenyuk said of the game-winner. "I saw an opening in the middle. I think I walked in quite well and had an open shot. Lucky for me it went in."
Max Pacioretty and P.K. Subban also scored for Montreal, which improved to 2-0 in the pre-season while outshooting a Colorado side with 11 NHL players dressed by 35-27.
Barrie and Gabriel Landeskog replied for Colorado in a fast-paced, end-to-end game.
The two teams meet again Friday night in Quebec City.
Galchenyuk, the third overall pick in the 2012 draft, spent most of his first two NHL seasons playing left wing, but is being given a look at centre in camp. He got 16:09 of ice time and had three shots on goal.
"I tried to make some plays," the 20-year-old said. "There were some turnovers, but that's part of the game. I still have to get better and adjust to it."
Thomas was not slated to play, but got in a second straight game when winger Dale Weiss developed stiffness in his neck and sat out. He responded with another strong game, using his speed to create several chances.
Coach Michel Therrien was impressed, even if the five-foot-nine son of former NHL sniper Steve Thomas remains a long shot to make the team.
"He competes, he makes things happen," said Therrien. "You notice him on the ice.
"It's still early in camp, but we like what we've seen of him."
Colorado opened the scoring at 12:59 of the first frame when Nathan MacKinnon won a battle behind the net with Alexei Emelin and fed Barrie in the slot for a quick, high shot over Carey Price.
Pacioretty wristed in a high shot on a power play 8:07 into the second, but Landeskog tied when he finished a tic-tac-toe play from MacKinnon and Jesse Winchester at 10:18.
Subban tied it again with a bullet from the point during a two-man advantage at 17:42.
Price allowed two goals on 10 shots before giving way to Peter Budaj, who stopped all 17 shots he faced. Berra went the distance for Colorado and faced 35 shots.
Montreal went 2 for 7 on the power play, although they failed to score on a two-man advantage in overtime.
"We're tryig to get better as the days go on," said Pacioretty. "We hadn't worked on power plays at all before (Thursday) morning when we went over it a bit, so it's nice to click."
The Canadiens announced that prospect Michael McCarron will be out six weeks with a shoulder injury suffered Tuesday against Boston.