Ville Husso made 29 saves in his Detroit debut, and Derek Lalonde won his first game as an NHL coach.
"I felt like we were on top of them the whole way," said Husso, who got his fourth shutout in 54 NHL starts. "It was one of those games you enjoy as a goalie. You trust the team is going to do a great job for you."
Michael Rasmussen had a goal and two assists, and Oskar Sundqvist had two assists for the Red Wings.
"I just like the way we played," Lalonde said. "I am a lot happier about the zero than I am about the three. There were times when it looked like it might get away from us, especially in the second period, but the guys hung in there."
Jake Allen made 37 saves for the Canadiens, who were coming off a 4-3 season-opening win against the Toronto Maple Leafs on Wednesday.
"I think they brought a lot of pressure against us," Montreal coach Martin St. Louis said. "They chipped a lot of pucks in and finished their checks. I think we'll learn some things from this game and be better for it."
Soderblom, who at 6-foot-8 is the tallest player in Red Wings history, jammed a rebound between Allen's legs to give the Red Wings a 1-0 lead at 2:33 of the third period.
"It's an unbelievable feeling," Soderblom said. "Husso was a wall back there and Derek is a great head coach. This was a lot of fun."