Taylor Hall scored for the third straight game, and Linus Ullmark made 30 saves for Boston (6-1-0), which has won the first three of a four-game homestand.
"We're finding different ways to win every night," Bruins coach Jim Montgomery said. "I didn't think tonight was a very good offensive game for us. I thought there were plays to be made that even our elite offensive players weren't seeing, but our checking is really improving, and we won with defense, and, of course, Linus was really good in net again tonight."
Wyatt Johnston scored, and Jake Oettinger made 26 saves for Dallas (4-2-1), which lost at the Ottawa Senators 4-2 on Monday.
"Back to back, tough situation. I thought we came out and played a real tough road game," Stars coach Pete DeBoer said. "I think they found a way to get a power-play goal, we didn't. They got a bounce in front of the net off a leg, we didn't, but I thought we played hard. We played a better game than we did in Ottawa in a back to back against a good team, so, you know, there's some positives there."
Stars defenseman Miro Heiskanen (upper body) was a late scratch. He was replaced by Joel Hanley, who had two shots in 12:14 in his season debut. DeBoer said Heiskanen is day to day and will be reevaluated when they return to Dallas.
"Tough loss with Miro, but we have six other [defensemen] that are here who are going to step in and get some more minutes," said Nils Lundkvist, who played 22:04 after averaging 17:07 in five games this season. "He's obviously almost a top five defenseman in this league, so tough loss, but you know, [we] tried our best, and I think we played a pretty solid game."