The goal was Briere's second of the game, sending the Sabres to their third straight overtime win and second in two nights.
Randy Robitaille scored twice for the Flyers, who lost their fifth straight game.
Philadelphia seemed poised to pull one out against an Eastern Conference rival after scoring three straight goals to take a 4-3 lead. However, with 2:59 left in regulation, Briere knocked a rebound past a diving Antero Niittymaki to tie the score.
The Sabres have tormented the Flyers since knocking them out of the first round of the playoffs last season. In October, Buffalo embarrassed the Flyers 9-1, scoring six goals in a second-period outburst, a loss that was the catalyst for general manager Bob Clarke's resignation and the firing of coach Ken Hitchcock.
The season only got worse for the Flyers, who entered with the fewest points and wins in the NHL.
And Philadelphia played this one without captain Peter Forsberg, still struggling to find an answer to the skate problem that's causing him discomfort to his surgically repaired right ankle.
For a while, it looked like more of the same blowout result. The Sabres scored three straight goals over the first and second periods to grab a 3-1 lead.
However, Philadelphia played with an energy and intensity that's been missing most of this season. They also showed up with a bit more aggression as Triston Grant, Mike Richards and Ben Eager all got in some punches - and five-minute majors - in three fights that energized the team.
Alex Picard started the comeback with his first NHL goal late in the second, with his shot from the point just slipping through inside the left post.
R.J. Umberger tied the score at 3-3 only 20 seconds into the third when he put a wrist shot right through Martin Biron's pads for his fourth goal of the season.
Robitaille's second goal came midway through the third period and capped the Flyers' rally back. He redirected a pass into the net for his third goal of the season and a 4-3 lead.
But it was not enough
Goalie Robert Esche allowed nine goals on 37 shots and played the whole game in the 9-1 loss. Niittymaki was much better in this one, stopping 32 shots. He was strong early in the game, turning away a barrage of shots that perhaps inspired his teammates.
Once the Flyers finally got a chance on offence, Robitaille one-timed a power-play goal to make it 1-0 and giving them a rare early lead.
The Sabres did their best to demoralize the Flyers, with Paul Gaustad tying the score in the first, and Jason Pominville and Drew Stafford putting Buffalo ahead 3-1 in the second.
Notes: The Flyers removed the interim tag from Paul Holmgren's title and made him general manager for the rest of the season. Holmgren became interim general manager in late October after Clarke resigned. Holmgren said he doesn't plan to trade Simon Gagne or Forsberg. ... The Flyers recalled C Ryan Potulny from the Phantoms, their AHL affiliate. ... D Denis Gauthier will have surgery Tuesday on his left shoulder. ... The Los Angeles Kings claimed C Marty Murray off waivers from Philadelphia. The 31-year-old Murray had 15 points with the Phantoms. ... Flyers C Petr Nedved's two assists give 400 in his career.