Galchenyuk scored at 3:37 of overtime, and the NHL-leading Canadiens beat the Detroit Red Wings 2-1 on Saturday night.
The Canadiens were outshot 28-14 after the first period.
"We got a really good start, but Mrazek was outstanding. Both goalies were outstanding, really," Montreal coach Michel Therrien said. "That's why it was 0-0 into the third period. I thought we gave them too much momentum in the second period, and we never really got it back."
Galchenyuk finished off a 2-on-1 by one-timing a pass from Alexander Radulov past Mrazek from the bottom of the left circle. It was Galchenyuk's ninth goal.
"Pricey makes the great save, and I just took off, because I knew Rads would get me the puck," Galchenyuk said. "He made a great pass, and I was just trying to keep the shot down. I didn't want to shoot over the bar."
The Red Wings won 5-4 in New Jersey on Friday night in overtime.
"It's always tough but hey, listen, we've caught a lot of teams on back-to-backs in here. There's no excuse," Abdelkader said.
"I think we were terrible first period but it's always tough when you get in late and turn around and play the next night when the other team's sitting here waiting for you."
Red Wings coach Jeff Blashill said he likes how his team is playing.
"It's encouraging for sure. When you're starting to play good hockey you can see it and I think we're starting to play good hockey," he said. "I really like our line combinations. I think they mesh well together."
Gallagher tied it at 1 with 8:05 left in the third period when he tipped in a shot by Tomas Plekanec. It was Gallagher's first goal in 16 games and No. 5 on the season.
Abdelkader, appearing in his 500th career game, put Detroit in front 3:20 into the third period. He beat Price high on the glove side with a wrist shot from the high slot that deflected off the stick of Canadiens defenseman Greg Pateryn. It was Abdelkader's fourth goal.
Two Red Wings were helped to the dressing room in the second period.
Blashill said he would have updates on Smith and Bertuzzi on Monday.
"I have to take a look back on the replays but for sure, a couple questionable ones," Abdelkader said. "That's obviously a league matter and something the league will look into. I haven't really seen the full replay so I'm not going to really comment on that."
Detroit recalled G Jared Corveau from Grand Rapids of the American Hockey League because G Jimmy Howard suffered a groin injury in Friday night's 5-4 overtime win in New Jersey. Howard is expected to be out a week or so. ... Montreal F Charles Hudon sustained an upper-body injury during practice Friday morning and did not make the trip as a precaution.
Canadiens: Visit the Anaheim Ducks on Tuesday.
Red Wings: Host Dallas Stars on Tuesday