Rasmussen had a goal and an assist, and Ville Husso made 20 saves in his fourth straight start for the Red Wings (21-18-8), who have won three of four and visit the New York Islanders on Friday.
"We're 3-1-1 in our last five [games], so a really good segment of 7 of 10 points and we keep climbing," Detroit coach Derek Lalonde said. "The guys wanted to play important games late in the season, here we are before the All-Star break right in the middle of a bunch of teams, and a team we're chasing in New York tomorrow."
Rafael Harvey-Pinard had two goals and an assist, Michael Pezzetta had a goal and an assist, and Alex Belzile had two assists for the Canadiens (20-25-4), who have lost three of four.
"Of course you want to win at the end of the game, but when I think about our line, I think we had a great forecheck tonight," Harvey-Pinard said. "We were on the puck, a lot of shots on net too, so I think we did a good job tonight."