Philadelphia trails the best-of-7 series 3-2 and will host Game 6 on Sunday.
Matt Murray made 21 saves for the Penguins, who led 2-1 late in the second period.
"The elimination game is probably the hardest game of them all," Murray said. "I thought we had a pretty good game today and we just have to stick to our mindset. Keep on our toes and keep doing what we need to do."
Michal Neuvirth made 30 saves for the Flyers in his first start since Feb. 16.
"I felt all right. I was battling all 60 minutes," Neuvirth said. "We had a great first period, then took some penalties in the second. But we finished strong and we were really happy with the win. … I like playing in the playoffs, like facing the pressure, but it's only one game and we came here to win a hockey game. We did that. Now we have to win the next one."