The Red Wings struck first, when Dylan Larkin had the puck behind the net and fed Tyler Bertuzzi in the slot to put Detroit ahead at the 3:21 mark.
A few minutes later, with Brendan Gallagher in the box for cross-checking, Phillip Danault broke away and managed a shot on Red Wings netminder Jonathan Bernier, but was denied.
The Habs had a power play opportunity of their own with 3:07 left to play in the first, but couldn't capitalize.
Montreal headed to the room down 1-0 after 20, but was leading 12-7 in shots.
The Canadiens were once again the stronger team in the second, outshooting the Red Wings 10-5, but couldn't manage to get anything by Bernier and were still trailing at the end of the middle frame.
Early in the third, the Canadiens buzzed and had a flurry of eye-popping chances in the Detroit end, but Bernier and the skaters in front of him somehow were able to hold onto their shutout bid.
The Red Wings doubled their lead with 12:17 left in regulation. With Riley Barber in the box for slashing, Mike Green potted his second of the season to make it a 2-0 game.
The Habs pulled Carey Price late in the final stanza, and capitalized on their chance when Tomas Tatar rang it in to cut the Wings' lead to 2-1 with 46.4 seconds to go.
Montreal couldn't complete the comeback, however, and the final score stood at 2-1 when the final horn rang.
