Rookie Matt Read, Scott Hartnell, and Jaromir Jagr scored in the second period, and Maxime Talbot added goals for Philadelphia, which led 4-3 in the third.
The Flyers (16-7-3) scored four times on 10 shots bridging the first and second periods after falling behind 3-0 to win their third straight.
Philadelphia also climbed out of a three-goal hole on Friday at Anaheim and won on another overtime goal by Giroux, who added three assists against the Sabres. Ilya Bryzgalov made 20 saves.
Zack Kassian had a goal and an assist, and Ville Leino, Thomas Vanek, and Drew Stafford also scored for the Sabres (14-11-2), who have lost three of four.
Buffalo's Ryan Miller, playing in his second game after returning from a concussion/neck injury, stopped 29 shots.
The Flyers are an NHL-best 10-3-1 on the road. Buffalo has lost six of its last seven at home (1-4-2).
After a Sabres turnover in the Philadelphia end, Giroux skated in on Miller on a breakaway and slipped the puck in on a deke for the winner.
After Buffalo blew its three-goal lead and fell behind, Stafford tied it at 4 with 1:35 left in regulation - scoring his fifth goal of the season after the Sabres pulled Miller for an extra attacker.
The Flyers got within 3-2 at 5:17 of the second period when Read deflected defenseman Kimmo Timonen's slap shot from the left point and sent the puck squirting past Miller.
Hartnell tied it at 3 with 5:05 to go in the second when his wrist shot from the right faceoff dot deflected in off the skate of Buffalo defenseman Christian Ehrhoff.
Jagr gave the Flyers their first lead with his ninth goal with 2:12 left in the second, wristing in a shot from the top of the left circle to make it 4-3.
Former Flyers forward Leino staked the Sabres to a 1-0 lead with a power-play goal midway through the first period, capping a pretty tic-tac-toe passing play with Kassian and Luke Adam.
Buffalo doubled its advantage on Kassian's third of the season, and Vanek made it 3-0 just 42 seconds later with a power-play goal.
Talbot cut the deficit to 3-1 with his seventh goal with just 1 second remaining in the first period, slipping the puck past Miller from the low slot after the Sabres turned over the puck in their end.
NOTES: Philadelphia LW James van Riemsdyk returned after missing four games with an undisclosed upper body injury. ... The Flyers are in a stretch of 11 of 14 on the road. ... Buffalo opened a five-game homestand. ... Buffalo C Paul Gaustad missed his first game with an undisclosed upper body injury after he was hurt in a pileup that ensued after Nashville's Jordin Tootoo charged into Miller on Saturday. Tootoo received a two-game suspension for the play. ... The Sabres are without seven injured regulars. ... Buffalo LW Nathan Gerbe left early in the second period after he was checked into the boards from behind at the red line by Philadelphia D Marc-Andre Bourdon. Gerbe didn't return because of what the Sabres called an upper body injury.