It is Buffalo's longest winning streak since 2006-07, when it started the season with 10 straight victories.
"We talk about just being even-keeled, not being too high, not being too low, because there's going to be parts of the game we're not going to be able to control," Sabres coach Phil Housley said. "So how do we react to that adversity? Certainly, the belief, this group is getting tighter and tighter every game through this winning streak."
WATCH: [All Flyers vs. Sabres highlights]
Jeff Skinner scored his 14th goal in 15 games, and Carter Hutton made 23 saves for the Sabres (14-6-2).
Claude Giroux and Wayne Simmonds scored for the Flyers (9-10-2), who have lost four straight.
Alex Lyon
was relieved by Calvin Pickard to begin the second period after he allowed four goals on 12 shots in the first in his first NHL game this season. Pickard made eight saves.
"I feel bad for him. We let him down, the whole team," defenseman Christian Folin said of Lyon. "You shouldn't do that to your goaltender. It's frustrating. He's such a good goalie and such a great guy that we want him to play well. He's playing well, but we're putting him in [lousy] situations."
Skinner gave the Sabres a 1-0 lead 3:38 into the game when the rebound of a Jason Pominville shot bounced out to him in the slot.