Roope Hintz scored his 20th goal of the season, and Jake Oettinger made 25 saves for the Stars (23-17-2), who have won five of their past six games.
"They've been one of the best teams in the League for the last 10 years," Oettinger said of the Bruins. "It's always a good challenge, and I just want to show that I can be counted on in big games against those top teams. Whenever your team can put up goal support like that for you, it's huge. You just need a couple of key saves and the guys are going to do the rest."
Linus Ullmark allowed four goals on 15 shots for the Bruins (25-14-3) before he was pulled in the second period. Jeremy Swayman made 12 saves in relief.
"You've got to execute at an NHL level, especially against good teams," Boston coach Bruce Cassidy said. "They're really pushing it. We didn't do enough of that tonight. On the offensive side of it, we didn't do it either. The forward group, getting pucks behind them early to establish a forecheck, I thought we were stubborn that way.
"You put those two things together against a good hockey club that defends well, and it was going to be an uphill battle. We didn't figure it out."
Seguin drove the net and tipped in a shot that deflected off Bruins defenseman Urho Vaakanainen to give the Stars a 1-0 lead at 6:54 of the first period.