Jason Pominville and Maxim Afinogenov scored 1:39 apart early in the second period to open a 4-1 lead for the Sabres, who matched the 1975 club record for consecutive victories to start a season. Buffalo has also won a franchise-record 13 straight in the regular season.
Ales Kotalik also scored for Buffalo when he knocked in a loose puck after a gaffe by Boston goalie Hannu Toivonen. Thomas Vanek had the Sabres' other goal and Martin Biron had 26 saves.
Phil Kessel, Boston's No. 1 pick in this year's draft, scored his first NHL goal, and Wade Brookbank had the Bruins' other score.
Drury, held pointless for the first time this season in a 5-4 win over Carolina on Friday, put the Sabres ahead 1-0 on a slap shot from the top of the left circle 6:08 into the game.
After the Bruins tied it 1-1 on Brookbank's goal 1:54 later, Buffalo took the lead for good on Kotalik's goal at 12:53.
Pominville scored a power-play goal from down low after a nice feed from Vanek 1:17 into the second. Afinogenov made it 4-1 when he scored out of a scramble, firing a rebound over a sprawling Toivonen. Tim Thomas replaced Toivonen after the goal.
Kessel cut it to 4-2 on a wrist shot from the right circle.
Drury's second power-play goal and his ninth of the season made it 5-2 at 5:29 of the third.
Notes: The Bruins recalled C Nate Thompson from Providence of the AHL earlier in the day and he saw limited action. ... Boston D Brad Stuart left the game with a broken finger. ... It was the first part of a Buffalo-Boston sports weekend. The New England Patriots play at the Buffalo Bills on Sunday. ... As the clock wound down chants of 'Let's go Buffalo' could be heard clearly.