Alex Tuch, Mattias Samuelsson, Zach Benson and Josh Norris scored for the Sabres, who are the No. 1 seed in the Atlantic Division. Tage Thompson and Rasmus Dahlin each had two assists, and Alex Lyon made 25 saves.
The Sabres will face either the Montreal Canadiens or the Tampa Bay Lightning in the second round. Tampa Bay forced Game 7 in that series with a 1-0 overtime victory in Montreal on Friday.
Buffalo’s last series win came when it eliminated the New York Rangers in Game 6 of the 2007 Eastern Conference Semifinals.
David Pastrnak scored, and Jeremy Swayman made 22 saves for the Bruins, who were the first wild card from the East.
Tuch gave the Sabres a 1-0 lead at 3:25 of the first period. He scored on a tap-in near the right post off of Dahlin’s pass from the bottom of the left face-off circle.
Samuelsson increased the lead to 2-0 at 12:26, scoring with a wrist shot from above the left circle that got inside the near post with Swayman heavily screened.
Pastrnak cut the deficit to 2-1 at 1:54 of the second period. He created a turnover in the neutral zone with a hit on Ryan McLeod, then finished a 2-on-1 with a one-timer from the left circle after a pass from Pavel Zacha.
Benson made it 3-1 at 5:58 of the third period. Josh Doan outraced two Bruins for the puck in the left corner and sent a centering pass to Benson, who was all alone between the circles and scored to the glove side.
Norris added an empty-net goal at 16:40 for the 4-1 final.
