Simon Gagne scored on a power play with 7:08 left to cap a comeback from a three-goal deficit as the Flyers became only the third team in NHL history to win a series after losing the first three games.
Philadelphia will start the next round at home Sunday against another surprising conference finalist, the Montreal Canadiens.
Gagne, a major force since returning from a toe injury for Game 4, scored with only 18 seconds left in a power play after the Bruins were penalized for having too many men on the ice.
The Flyers capitalized when captain Mike Richards' shot from the right circle hit players in front of Bruins goaltender Tuukka Rask. The puck bounced and Gagne, stationed to Rask's left, flipped the puck over the goalie's right shoulder.
The only other teams to win a series after trailing 3-0 were the 1942 Toronto Maple Leafs, who beat Detroit, and the 1975 New York Islanders, who eliminated Pittsburgh. The other 159 teams that won the first three games in a series all won them.
The Bruins shot out to a 3-0 lead on power-play goals by Michael Ryder and Milan Lucic and another goal by Lucic, all within 14:10 of the first period. Then James van Riemsdyk scored for Philadelphia with 2:48 left in the first period before second-period goals by Scott Hartnell at 2:49 and Danny Briere at 8:39 to tie it.
Boston, having lost its previous two Game 7s, played aggressively at the start, and got a break when Hartnell was penalized for high-sticking and Ryder scored his fourth playoff goal on a rebound 8 seconds later.
Another Boston power play 3 minutes later led to another goal, this one by Lucic, who tipped in a pass across the crease from Dennis Wideman in the right corner.
Lucic struck again, scoring his fifth playoff goal five minutes later, on a shot from the right circle.
Flyers goalie Michael Leighton, who took over in Game 5 when Brian Boucher sprained the medial collateral ligament in his left knee, didn't let another goal past him.
Van Riemsdyk began the comeback with his first playoff goal on a soft shot that trickled by Rask. That was the first of nine consecutive shots by Philadelphia. One of them was Hartnell's second goal of the playoffs. Another was Briere's seventh playoff goal — on a wraparound.
There were no more goals — until Gagne sent the Bruins into an offseason wondering how it all fell apart.
