Filip Zadina scored the tiebreaking goal with 3:52 left in the third period, giving Detroit a 4-3 victory over Montreal on Tuesday night.
"We needed this win against them so bad," Zadina said.
The Red Wings are 3-0 against Montreal this season, but have won just eight of 41 games against the rest of the league.
"Yeah, that hurts," acknowledged Canadiens forward Tomas Tatar, who played in Detroit for seven seasons.
Montreal coach Claude Julien, meanwhile, refused to answer a question about losing all three games to Detroit.
"I'm just talking about tonight's game," Julien said.
The Red Wings had lost two in a row and 20 of their last 23, giving them the NHL's worst record by a wide margin.
Montreal has dropped seven straight games.
"When you get tired of losing enough, you do something about it," Julien said. "And hopefully, we're there."
Frans Nielsen got his second goal of the game with 8:41 remaining to pull the Red Wings into a 3-all tie. Earlier in the period, Victor Mete was credited with a go-ahead goal that went off Detroit defenseman Filip Hronek's skate.
Nielsen scored midway through the second and Robby Fabbri's wrist shot from the slot early in the third tied it at 2.
"We're up a goal going into the third and I think everyone in this room thought we were going to finish it off," Lindgren said. "We had a chance to put them away, but they score in the first minute and now it is a hockey game again. It came down to who made the biggest plays down the stretch and they did it."
Lehkonen made the most of one of the many mistakes by the Red Wings midway through the first period. He skated in front of a poorly passed puck from Hronek just inside Montreal's blue line and carried it up the ice to beat Bernier between his pads with a backhand.
Suzuki took advantage of extra time and space on a power play 6:31 into the second and scored to put the Canadiens up 2-0.
The Red Wings, though, rallied for a rare win, and Zadina's fist pump after his go-ahead goal showed how much each game still matters to their players and coaches.
Zadina connected on a one-timer in front off Adam Erne's pass from behind the net.
"He definitely has a shooting mentality," Detroit coach Jeff Blashill said. "I think it's a positive. There's times where he gets in that scoring square that even there's a potential for a pass to be made, but I never, ever talk to him about it because I'm not going to take away that shot-first mentality."
The crowd in Detroit sang the Canadian national anthem because the arena had technical difficulties with the audio. ... Montreal has its longest losing streak since dropping a season-high eight in a row. ... Ilya Kovalchuk has at least one point in each of his two games with the Canadiens, who signed him last week. ... Detroit's Givani Smith got his first NHL assist in his seventh career game. ... Nielsen had only one goal in 38 games before scoring twice against Montreal in his first multi-goal game since his hat trick.
Canadiens: Host the Edmonton Oilers on Thursday night.
Red Wings: Host the Ottawa Senators on Friday night.
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