Following a turnover by New Jersey defenseman Marek Zidlicky, Briere unleashed a shot from near the left circle that eluded Devils goaltender Martin Brodeur, who was screened by the Flyers' James van Riemsdyk on the play.
Briere's game-winner came after officials ruled he had kicked the puck into the net on an apparent winning score only minutes earlier.
Briere and van Riemsdyk each scored in the second period and Claude Giroux also found the net for the Flyers, who grabbed a 1-0 lead in their Eastern Conference semifinal series against the Devils.
Ilya Bryzgalov turned aside 23-of-26 shots to earn the victory.
Brodeur finished with 32 stops in the loss.
Game 2 in the best-of-seven series is set for Tuesday in Philadelphia.