Boston joined the Montreal Canadiens as the only NHL teams to reach the milestone.
Glen Murray and rookie Lee Goren scored 20 seconds apart in the final minute of the opening period to extend Boston's lead to 3-0.
Murray ripped a slap shot past Martin Biron off a pass from Brian Rolston with three seconds left on a two-man advantage. Off the ensuing faceoff, Goren got a perfect pass from Ivan Huml, streaked into the right faceoff circle and beat Biron to the short side for his first NHL goal since March 10, 2001.
Mike Knuble opened the scoring at 5:21 when he shot the puck past a screened Biron.
Boston went three for nine on the power play and has converted 13 of 42 chances over the last eight games.
Buffalo's lone goal came at 1:35 of the second period when Curtis Brown fought off a check long enough to put a snap shot past former Sabre Steve Shields.
Shields turned aside 22 shots and has won four of his last five starts.
The Bruins, who have won five straight at the FleetCenter, also recorded the 1,500th home win in franchise history.