Alex Nedeljkovic made 38 saves for Detroit (4-4-2), which is 0-2-1 in its past three games and 0-3-0 this season without forward Tyler Bertuzzi, who is unable to play in Canada because he is unvaccinated against COVID-19.
"I'm assuming if I'm their coach I would be happy with the way they played," Red Wings coach Jeff Blashill said. "But I'm not their coach. I'm our coach and I wasn't happy with the way we played. All I know is what we were doing wasn't good enough. I know that for sure."
Along with Bertuzzi, the Red Wings were also without captain Dylan Larkin, who did not play for personal reasons.
"Whether those guys are in or not, we've got to try to find ways to score goals and try to be in games," Detroit defenseman Danny DeKeyser said. "I thought 'Ned' gave us a chance. He made some big time saves, but we've got to put the puck in the net a little bit more."
Suzuki scored his first goal of the season to put Montreal ahead 1-0 at 2:06 of the first period, batting in his own rebound after his initial backhand from in front was saved by Nedeljkovic.
"It's definitely a little weight off of my shoulders," Suzuki said. "I've had some chances, they just haven't gone in. So hopefully that's going to spark something."
Josh Anderson made it 2-0 at 9:18 of the first. He took a stretch pass off the boards from Suzuki and scored on a shot under Nedeljkovic's glove from the left circle.
Gallagher shot into an empty net with 2:01 remaining in the third for the 3-0 final.
"[This season's] been frustrating, obviously, but you know the only way to get through it is to keep working, keep grinding away. Once you do that, you're going to pull a lot of guys into the fight with you," Anderson said. "I thought tonight everybody was on board, but we got to get back at it tomorrow in practice, keep working hard and repeat that next game."