Patrice Bergeron scored a shorthanded goal for the Bruins (36-11-12), and Tuukka Rask made 25 saves to extend his home point streak to 20 games (14-0-6).
WATCH: [All Red Wings vs. Bruins highlights]
The Bruins, who won their second straight game and are 8-1-0 in their past nine, had lost their prior five games with the Red Wings, including 3-1 at Detroit on Feb. 9.
"We knew what our last couple against these guys what the result has been, so that's added incentive," Bruins forward Charlie Coyle said. "Every point's huge from here on out, as we all know. And we want to be playing our best hockey heading in here. That's what we tried to bring tonight, especially against a team who's had our number. So it definitely feels good to kind of play that way and win playing the right way and feeling good about ourselves."
Jonathan Bernier made 37 saves for the Red Wings (14-42-4), who lost their third straight game and have two wins in their past 15 games (2-12-1). Bernier has lost his past three starts.
"Like I said even when I was winning, you've just got to focus on your own job," Bernier said. "You can't let three, four losses in a row get to you, you just got to keep working hard, keep doing your thing and give the best chance for your team to win some hockey games."