It was the second straight three-point game for DeBrincat, who had three assists in a 5-2 win against the Calgary Flames on Monday.
J.T. Compher and Andrew Copp also scored for the Red Wings (38-23-8), who have won two straight after losing five of six (1-3-2). John Gibson made 32 saves.
Detroit is tied with Montreal for third place in the Atlantic Division and is also tied with the Boston Bruins for the two wild-card spots into the Stanley Cup Playoffs from the Eastern Conference.
“This was definitely a playoff atmosphere,” Red Wings coach Todd McLellan said. “On the ice, there were a lot of competitive battles and emotion, but you could feel it off the ice as well, there was so much energy in the building.”
Juraj Slafkovsky scored for the Canadiens (37-21-10), who have lost three of four. Dobes made 25 saves.
“I thought we played a decent game,” Slafkovsky said. “We had many opportunities to score more goals than we did, we needed to do it. It was a nice hockey game to play in, but it just stinks we’re not the ones smiling right now.”
Montreal coach Martin St. Louis said, “We were right there despite a lot of bad luck. We played a mature game and we were in control for a long time.”
Slafkovsky put the Canadiens up 1-0 with a power-play goal at 17:45 of the second period. Cole Caufield threw the puck on net from the goal line, and Slafkovsky pounced on the rebound to beat Gibson over the left shoulder with a snap shot that went bar down.