The Bruins scored three times in the third period to extend their point streak to 13 games (9-0-4) and remain the only NHL team without a regulation home loss (12-0-5).
Robin Lehner made 37 saves for the Blackhawks (11-12-5), who ended their three-game losing streak.
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"Well obviously it's a good feeling. I mean, we knew this was a good challenge for us and a great opportunity," Lehner said. "Been in a little bit of a slump coming in to [play] probably the best team in the League at the moment in their building. Obviously we would like to win in it regulation, but we made some mistakes and they capitalized on it. … They're a good team, we battled hard, made some mistakes, they capitalized on it, and eventually we were rewarded, so it's a great win."
Tuukka Rask made 27 saves for the Bruins (20-3-6), who won their previous three games despite trailing or being tied in the third period.
"I don't know that it's sustainable. Maybe if you can keep it tied and then in the third find that crack and try to expose it. We've got game breakers that can do that," Bruins forward David Backes said. "But certainly digging the hole 2-0, letting them score [17] seconds into the third, was not a recipe for success.
"That being said, we showed some great character and found a way to get one point out of it, and whatever you say about overtime, they made a play and you know you got all the momentum and you hope to finish off the job of all the hard work to getting that game back to even."
Ryan Carpenter scored a shorthanded goal on a rebound shot at 18:14 of the first period for a 1-0 lead.