York scored on a shot from the blue line that went through traffic in front, off the right post and in for his first career Stanley Cup Playoff goal.
The Flyers, who are the No. 3 seed from the Metropolitan Division, will face the Carolina Hurricanes, the top seed in the East, in the second round.
Dan Vladar made 42 saves for the Flyers, who advances in the Stanley Cup Playoffs for the first time since defeating the Montreal Canadiens in six games in the 2020 Eastern Conference First Round.
Arturs Silovs made 31 saves for the Penguins, the No. 2 seed from the Metropolitan.
Each team had an opportunity on the power play in the first period. The Penguins got the first chance when Flyers defenseman Jamie Drysdale was called for interference but managed just three shots on goal.
The Flyers' chance came when Noel Acciari was called for holding but they managed just one shot.
Philadelphia got the first big scoring chance of the second period during a Pittsburgh power play when Christian Dvorak nearly finished a give-and-go with Sean Couturier on right post at 6:12, but Silovs made a sliding pad save.
The Penguins answered with a strong chance for Egor Chinakhov but his shot from the left face-off circle hit the post at 6:49.
Flyers forward Matvei Michkov, back in the lineup after being scratched for Game 5 on Monday, had a chance on a breakaway but Silovs got a piece of the shot with his glove at 15:26.
Philadelphia started the third period with a power play after Kris Letang was called for roughing at the end of the second period but managed one shot on goal.
