Dustin Tokarski made 27 saves for Buffalo (31-39-11), which had won four in a row.
"I think it was honestly a pretty even game, like we had opportunities, lots of shots, and they just found a way to put it in the back of the net. We didn't," Sabres center Dylan Cozens said. "There's areas to improve in every way, and definitely things we could have done better in that game. It's a frustrating one to lose."
Buffalo outshot Boston 12-6 in the first period, which had no goals.
"I thought we had opportunities to score in the first, and didn't," Granato said. "I thought we played real well in the first, and then we didn't look like ourselves in the second and third at all. I don't know if it was an energy thing or what it was, but the game slipped away at that point."
Bergeron put the Bruins ahead 1-0 at 6:16 of the second when he put in a loose puck in front of the crease. The Sabres could not clear it after Tokarski stopped shots by Marchand and Jake DeBrusk, and the puck went right to Bergeron.