Brad Marchand and Milan Lucic also tallied for the Bruins, who have won three in a row and six of their last seven.
Tyler Ennis recorded the lone goal for the Sabres, who had taken a 7-4 decision in Boston on Jan. 31 in the clubs' first meeting.
Ryan Miller played well in defeat, stopping 36 shots.
"I think we started to show our fatigue around the midpoint," Miller said. "They're a tough team to play against and they certainly were going to make it so we weren't going to have the opportunity to score as many goals as we did last time."
Bergeron put the Bruins ahead at the 7:52 mark of the third period while on the power play. He alertly beat a pair of Sabres defensemen to a puck which caromed off the end boards and back out into the left circle, and beat Miller high to the glove side.
Miller was called to the bench for an extra attacker in the final minute, and Lucic potted the insurance marker into the empty cage.
Buffalo was given a brief advantage when Boston defenseman Andrew Ference was called for high sticking 14 seconds later, but failed to convert.