Jake DeBrusk scored in his fifth straight game and in the tiebreaker for Boston (36-17-8), which extended its point streak to 12 games (9-0-3). Jaroslav Halak made 31 saves.
"It feels good," DeBrusk said of the winning streak, which includes four straight on the road. "It's lots of teambuilding right now, and guys are feeling good about themselves. It's always nice to win."
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Boston's winning streak is its longest since March 2-22, 2014, when it won 12 in a row.
David Backes scored the winning goal in the bottom of the sixth round for Boston, which extended its lead to four points over the Toronto Maple Leafs for second place in the Atlantic Division.
"Truthfully, I was still in shock that [Bruins coach Bruce Cassidy] called my name with some of the guys who hadn't gone yet," Backes said. "So I thought there was, at least, maybe a handful before me. But I got the call, went out there. I'm a shooter by nature.
"[Bruins forward Brad Marchand] said, 'You got low glove all day if you come in from the six side.' I went in there and I thought the glove was a little high, I went low, and it worked out."