Trevor Zegras and Owen Tippett also scored for Philadelphia (15-8-3), and Travis Sanheim and Matvei Michkov each had two assists. Samuel Ersson made 24 saves for the Flyers, who have won six of their past eight games.
Jason Zucker and Bowen Byram scored for Buffalo (11-12-4), which was playing the first of a six-game road trip. Colten Ellis made 30 saves.
Zucker scored from the slot for a power-play goal that gave the Sabres a 1-0 lead at 4:08 of the first period.
The Flyers took the lead with three goals in a 59-second span.
Konecny started the run when he tied the game 1-1 at 8:26 with a power-play goal from above the left face-off circle.
The Sabres challenged for goaltender interference but after a replay review the goal counted. Buffalo was penalized for the unsuccessful challenge, and on the ensuing power play Zegras’ pass attempt from the right side went off the skate of Sabres forward Ryan McLeod and past Ellis to put Philadelphia ahead 2-1 at 9:04.
Brink made it 3-1 at 9:25 when he scored from the side of the net on the rebound of a Cates shot.
Cates put the Flyers ahead 4-1 at 1:45 of the second period when he got to the front of the net and redirected Brink’s centering pass.
Byram scored from the right face-off dot to make it 4-2 at 11:48.
Tippett batted in his own rebound to make it 5-2 at 12:43.
Zach Benson scored for the Sabres with 7:09 remaining in the third period, but the goal was overturned after the Flyers challenged for offside.
Flyers defenseman Cam York left the game with 3:10 to play in the second period because of an undisclosed injury.
Flyers score 3 goals in under 1 minute, cruise past Sabres
