Trailing the best-of-seven Eastern Conference quarter-final 3-0, the Penguins used a Jordan Staal hat-trick, two goals from the NHL's leading scorer Evgeni Malkin and captain Sidney Crosby's goal and two assists to outmuscle the hosts.
The series now shifts to Pittsburgh for Game Five on Friday with the Penguins still facing an uphill battle as they try to become just the fourth team to overturn a three-game deficit, a feat the Flyers themselves achieved in 2010.
"It's one win and we came here today to try to stay alive so it was a good effort by everyone and we'll continue in Pittsburgh," Crosby said.
In Los Angeles, Daniel Sedin returned from a 12-game absence with a concussion to help keep the Vancouver Canucks' season alive with a 3-1 win over the Kings.
Sedin chipped in an assist, goaltender Cory Schneider made 43 saves and top-seed Vancouver cut their best-of-seven series deficit to 3-1 and avoided being swept.
Game Five is on Sunday in Vancouver.
In Ottawa, the Senators climbed out of 2-0 first period hole against the top-seeded New York Rangers to claim a 3-2 overtime win on a goal from Kyle Turris 2:42 into the extra session.
The win levels the Eastern Conference series at 2-2 ahead of a trip back to New York for Game Five on Saturday.
"We know what's at stake, now it's a best-of-three and we go back home," New York's Ryan Callahan said. "We dealt with an OT (overtime) loss before and we responded and we have to do the same now and get ready to go Saturday night."
A sold-out crowd in Philadelphia was strapped in for another wild ride with the ill-tempered series highlighted by crunching hits and suspensions.
The Penguins quickly found themselves in trouble by taking a penalty just 17 seconds after opening faceoff and the Flyers quickly made them pay with Claude Giroux notching his fifth goal of the series.
The Penguins hit right back, however, Malkin leveling with his first strike of the play-offs followed by another from Matt Niskanen.
Powerplay goals by Kimmo Timonen and Jakub Voracek put the Flyers back in front but that would be the last lead the home team would enjoy as the Penguins reeled off eight unanswered goals.
Crosby and Staal scored a little more than a minute apart to give Pittsburgh a 4-3 edge going into the first intermission, then put the game away with a five-goal explosion in the second.
Staal led the charge by scoring twice, with Kris Letang, Steve Sullivan and Pascal Dupuis also finding the back of the net. Malkin completed the rout with the only goal of the third period.