Joel Farabee scored the only goal of the shootout, and Carter Hart made 26 saves through overtime for the Flyers (10-5-2), who have earned at least one point in their past six games (5-0-1).
Five of those six games have gone to overtime or the shootout, including a 3-2 shootout win at the Toronto Maple Leafs on Saturday.
WATCH: [All Flyers vs. Bruins highlights]
"Back-to-back this weekend, and it was against two tough teams, but we battled hard for 120 minutes," Hart said. "Back-to-backs can be tough, especially with travel, but we handled it really well, we came out hard both games. They didn't have anything for the first two periods, and I think that's just a good character win for us tonight, especially on back-to-backs because you're always battling the fatigue factor. But clearly that wasn't a factor for us tonight."
Jaroslav Halak made 27 saves for the Bruins (11-3-3), who came back from down two goals in the third period but have not won in their past three games (0-2-1).