Thomas Vanek had two goals and two assists, and Derek Roy scored twice for the Sabres (6-0), who posted a six-goal second period and are two wins shy of matching their best start set in 1975. Buffalo has also won 11 straight regular-season games, tying the franchise record established 21 years ago.
Also scoring for the Sabres were Chris Drury, who extended his point streak to six games (seven goals and three assists), Jiri Novotny, Jaroslav Spacek and Henrik Tallinder. Buffalo had its biggest offensive output since a 10-1 win over Los Angeles last January.
Jeff Carter spoiled Ryan Miller's shutout bid by scoring 2 minutes into the third period, but the Flyers have managed just 12 goals in six games.
Philadelphia (1-4-1) was so inept that it failed to put a puck on net during a first-period penalty shot. Mike Richards went wide to the left in an attempt to draw out Miller, but the goalie stayed in position, leaving Richards unable to get off a shot.
After a scoreless opening 20 minutes, Vanek sparked the goal surge, converting his own rebound 37 seconds into the second period. By the time the frame was over, Buffalo had scored six times on 12 shots, converted three of four power-play chances, and ended the period by scoring three times in a 2 1/2-minute span.
The Sabres, coming off a 7-4 win over the New York Rangers on Saturday, added three more in the first 5 minutes of the third period.
It was the first meeting between the teams since Buffalo beat Philadelphia 7-1 in Game 6 to win last year's first-round playoff series. And this game was reminiscent of Buffalo's 8-2 drubbing of the Flyers in Game 2 of that series. The Sabres again showed their speed was too much for Philadelphia's plodding defence.
That was particularly evident when Afinogenov capped the second-period run. The speedy winger went end-to-end, manoeuvered around a flat-footed Derian Hatcher, and jammed the puck past a helpless Robert Esche.
Esche, making his first start since the a season-opening 4-0 loss at Pittsburgh, played the entire game, allowing all the goals on 37 shots.
The nine goals allowed were the most by Philadelphia since a 9-4 loss at Pittsburgh on Feb. 9, 2001. The six in the second period matched a franchise worst, last done against New Jersey in March 1993.
Notes: Flyers D Mike Rathje missed his fifth straight game with a back injury. He is hoping to return at Tampa Bay on Thursday. ... The Flyers have failed on their last four penalty shots and are 12-of-33 overall. Miller has not allowed a goal on two penalty shots. The Sabres have yielded 17 goals on 40 chances. ... The Sabres' six-goal period was three short of a franchise record and their most since scoring six against Ottawa in October 1992.