Jonathan Bernier made 19 saves for Detroit, which swept the four-game season series. It is the first time the Red Wings have swept a series of at least that length against the Canadiens.
"It's one of those things you can't explain," Red Wings coach Jeff Blashill said. "It isn't like we have great matchups against them, and before this, there was a long stretch where they totally owned us."
Nick Suzuki had a goal and an assist for Montreal (27-27-8), which has lost five straight (0-4-1) and is tied with the Buffalo Sabres for fifth in the Atlantic Division, eight points behind the Toronto Maple Leafs for third. Carey Price made 21 saves.
"We had a lead here before and we couldn't hold it, so we knew what we had to do," Suzuki said. "I'm putting a lot of that on me."
Nate Thompson gave the Canadiens a 1-0 lead at 5:59 of the first period, tapping in a Nick Cousins pass. Montreal forward Paul Byron, who missed the previous 42 games with a knee injury, stole the puck from Athanasiou to start the play.
"It felt good to be back out there," Byron said. "It would have been better to come back with a win."