An empty-net goal by Jeff Carter with 25 seconds left sealed the victory after third-period goals by Chicago's Dave Bolland and Brian Campbell turned a seemingly comfortable 4-1 Flyers' lead into a 4-3 nailbiter.
The victory sends the NHL championship series to Game Five on Sunday in Chicago, where the Blackhawks won the opening two contests, but Flyers coach Peter Laviolette was confident.
"I like our game. I like what we're doing," he told reporters after the first game of the series to be decided by more than a one-goal margin. "I thought we could have won both games (in Chicago)."
The fired-up Flyers looked on their way to a romp after taking a 3-1 first-period lead, boosted by unassisted goals from captain Mike Richards and Matt Carle.
What appeared to be the finishing touch was supplied by Ville Leino, whose third-period goal made it 4-1 before the late charge by the Blackhawks.
"We battled all game but we were too generous to them in the first period," said Chicago coach Joel Quenneville. "The goals were the types of goals we don't normally give away."
It was the seventh successive playoff win for the Flyers in front of their raucous orange-clad home crowd, which included US Vice President Joe Biden, who hails from the nearby state of Delaware.
The thunderous cheering, however, soon gave way to anxiety as first Bolland and then Campbell, with 4:10 left in the game, got the puck past Philadelphia goalie Michael Leighton.
Chicago pulled Finnish goalie Antti Niemi with a minute to go and pressed hard for an equalizer, but the puck came free and Carter sealed the crucial victory with an empty-net goal.
The Flyers opened the scoring with a lightning strike after a high-sticking penalty against Tomas Kopecky.
Five seconds after the Chicago right-winger was sent to the box, Richards stole the puck from Sweden's Niklas Hjalmarsson behind the net and wrapped it around the post and past Niemi at 4:35 for a 1-0 lead.
Philadelphia took advantage of another Hjalmarsson mistake 10 minutes later when the Swedish defenseman tried to clear a rebound in front of the net and instead delivered the puck directly to Carle, who snapped it home to make it 2-0.
Chicago clawed back in the action-packed first period on a goal from Patrick Sharp at 18:32, but 51 seconds later Claude Giroux, who scored the overtime winner for the Flyers in Game Three, restored the two-goal advantage.
After a scoreless second period, Leino bounced a shot off the back of Chicago's Kris Versteeg and into the net to make it 4-1 before the Blackhawks battled back to make it close.
"They came hard but thank God we won," said Richards, who helped Canada win ice hockey gold at the Vancouver Olympics.
"It was tough to be up three goals. You relax and all of a sudden 'boom, boom', it's one goal."
