DETROIT — Montreal coach Claude Julien acknowledged the Canadiens can benefit by losing, increasing their chances in the NHL draft lottery.
Julien, though, insisted coaches and players are wired to win and refuse to compete with any other goal in mind.
Nicolas Deslauriers' second goal put Montreal ahead late in the second period and they held on to beat the Detroit Red Wings 4-3 on Thursday night.
The Original Six teams are out of the playoff race, finishing up the season playing only for pride.
"Both teams want to win. It's engrained in us," Julien said. "I've been told — I can honestly tell you — to try to win every game we can."
Antti Niemi had 23 saves for the Canadiens, started in place of struggling star Carey Price.
Detroit's Jared Coreau stopped 24 shots, giving Jimmy Howard the night off.
Montreal took advantage of the Red Wings turning the puck over, including early in the third period when Artturi Lehkonen scored to create a two-goal cushion.
"We're always trying to force turnovers and play a fastbreak game," Lehkonen said. "We got some opportunities and we did a good job finishing them."
Darren Helm scored less than a minute later to pull Detroit within a goal, but it couldn't' score again to extend the game.
Montreal had won just two of its previous 10 games and will miss the playoffs for the second time in three years.
"I'm not used to losing. I don't like to lose," Julien said. "But at the same time, I have to be objective and look at the situation and there were some challenges along the way that we didn't expect, a number of injuries, and players having to move up in the lineup in areas they weren't quite ready for."
The Red Wings have lost two straight and 15 of their last 19 games. They will be relegated to watching the postseason for a second consecutive season after earning a spot in the playoffs 25 straight times.
"We've found ways to lose too many times this year," Detroit defenseman Jonathan Ericsson said. "We lost a lot of one-goal games after leading games in the third. And, it's just not acceptable that we didn't close out more games."
The storied franchises hope they're fortunate enough to get the No. 1 pick overall to likely draft Swedish defenseman Rasmus Dahlin.
Detroit wants to rebuild around Dylan Larkin, who split two Canadiens on a rush and beat Niemi with a backhander late in the first to make it 1-all after Deslauriers had his first goal early in the game.
"Dylan continues to build his game," Detroit coach Jeff Blashill said. "That goal, I think, is a good sign for us."
Tyler Bertuzzi put the Red Wings ahead early in the second, but they lost the lead as they have many times this season.
Brendan Gallagher pulled the Canadiens into a tie midway through the second period and Deslauriers' 10th put them ahead with 5:21 left in the period.
"It's been a tough year so this was a nice bonus at the end of the year," Deslauriers said.
NOTES: Montreal D Jeff Petry was cheered on by at least one fan in the stands. His father, Dan Petry, an 18-game winner for the 1984 World Series champion Detroit Tigers, attended the game. ... Coreau, who has spent much of the season in the AHL, is 0-5 with the Red Wings this season. ... Gallagher has a team-high 31 goals, a double-digit lead over the rest of his teammates and seven more goals than he scored in any of his previous five seasons. ... Larkin has a five-game points streak.
Canadiens: Wrap up the season Saturday night at Toronto.
Red Wings: End the season at home against the New York Islanders on Saturday night.