Thomas Chabot and Ryan Dzingel scored for the Senators (15-23-9), who lost their fifth in a row.
"We knew it was going to be tough, because when you look at [Boston] in video, they've got four lines [of] bigger bodies that have got some speed too," Ottawa coach Guy Boucher said. "They're quick, they're able to hang on to pucks a lot in the offensive zone, which makes it very tough, first of all, to get the puck and be first on it, and once they're first on it, they're hard to handle."
Boston outshot Ottawa 20-7 in the first period but trailed 1-0 on a goal by Thomas Chabot at 12:00.
"We've had teams do that to us," DeBrusk said. "We were shooting everything. Credit to their goaltender, he was standing on his head. The message in the room was just to keep firing pucks an eventually they'll go in.
"I think that it was just a matter of just staying with it and not feeling sorry for ourselves, but to go get it."
Danton Heinen tied the game 1-1 on the power play at 11:35 of the second period when he waited for an airborne puck to come down and timed his shot.
"You want to be a consistent player," said Heinen, who ended an eight-game goal drought. "You want to be helping out every night, and sometimes it doesn't go in, but that was definitely nice to get that one."
Tim Schaller scored on a shorthanded breakaway 1:58 into the third period to give the Bruins a 2-1 lead. Dzingel tied it 2-2 20 seconds later on the power play.
The Bruins were without forward Brad Marchand, who served his first of a five-game suspension for an elbow against New Jersey Devils forward Marcus Johansson on Tuesday. Anders Bjork moved between the top two lines to take Marchand's place.
"I wanted to keep as much continuity going into the game, but in game make those changes," Bruins coach Bruce Cassidy said. "We're not going to have [Marchand] for four more games, so someone's going to have to go out there. We may rotate, but we prefer to keep one guy if we could."
