FIRST PERIOD
The Bruins took the early lead when Brad Marchand, who was working behind the net, slid a pass through Luukkonen's pads from below the goal line to Bergeron who finished it to put Boston on the board.
"That first one (goal) is on our line. That can't happen to start the game," forward Zemgus Girgensons said. "We've talked about staying five-tight and we just have gotten away from those little details."
Hathaway made it 2-0 when he took a stretch pass from Jakub Zboril and slipped behind the Sabres defense and beat Luukkonen on the rush. Later in the period, DeBrusk scored for the Bruins to make it 3-0 with 8:20 to play.
Hathaway went off for slashing at 13:05 to give the Sabres the first power play of the period. Jack Quinn had a chance for a one-timer in between the circles as the penalty expired but was denied by Swayman.
The Sabres got a second crack with the man advantage when Bergeron was nailed for holding at 17:02 but couldn't find the back of the net.
SECOND PERIOD
Buffalo got a pair of power-play chances in the second period but couldn't make a dent in the Boston lead. Pavel Zacha went to the penalty box for interfering with Victor Olofsson, and JJ Peterka drew a slashing penalty on Zboril in the final two minutes, but the Sabres couldn't solve Swayman.
Boston appeared to extend its lead to 4-0 less than five minutes into the period when Tyler Bertuzzi redirected a rebound past Luukkonen. After a short review, officials determined Bertuzzi kicked the puck into the net.
Three minutes later, Hampus Lindholm scored to officially give Boston a 4-0 lead.
Frustrations boiled over when Dylan Cozens and Boston's Trent Frederic dropped the gloves with 6:34 to play in the period. Each was sent off with five-minute major for fighting.
Zboril went back to the box for slashing with 1:15 left, but Casey Mittelstadt was called for slashing in a scrum as the second period ended to negate the man advantage.
Buffalo finished with four shots in 7:15 of power-play time.
THIRD PERIOD
Swayman made a pair of stellar saves to hold the Sabres scoreless in the early stages of the third period. He denied Quinn and Peterka on consecutive chances and then robbed Peyton Krebs on the doorstep.
Pastrnak and Coyle each scored midway through the third period as Boston pulled away, and McAvoy closed out the scoring with 2:01 to play.