Sidney Crosby scored his 14th for Pittsburgh, while Riley Sheahan also scored for the Penguins, who lost their second straight and seventh of 10. Casey DeSmith made 22 saves.
Weise gave Philadelphia a 3-2 lead 51 seconds into the third period with a short-handed goal. He beat DeSmith between the pads on the breakaway for his second goal this season. The Penguins have allowed a league-worst six short-handed goals.
Stolarz kept the Flyers in front when he stopped Derek Grant on a short-handed breakaway later in the period. Voracek sealed it with an empty-netter.
It was the first meeting of the season between the cross-state rivals. It was also the first game since the Penguins swept the regular-season series and eliminated the Flyers in the first round of the Stanley Cup playoffs last spring.
The Flyers, who started the day last in the Eastern Conference, fired general manager Ron Hextall earlier this week in addition to their assistant general manager and an assistant coach in an organizational purge.
Crosby opened the scoring 39 seconds into the game. He finished a 2-on-1 with a one-timer on a pass from Jake Guentzel. Crosby, who recorded his 11th career hat trick Wednesday against Colorado, has 14 goals and 24 points in his last 16 games. Crosby and Guentzel are both riding a four-game point streak.
Konecny evened the score when he beat DeSmith to the blocker side on a breakaway. Konecny has points in five of his last six games.
The teams traded goals 1:03 apart in the second period. Sheahan gave Pittsburgh a brief lead and Giroux tied it on a one-timer from a sharp angle near the goal line.
NOTES: Patric Hornqvist returned for Pittsburgh after missing three games with a concussion. … Flyers F Jori Lehtera played in his 300th NHL game. He was a healthy scratch the previous three games. … The Flyers recorded their first power play in eight periods on Saturday. Their most recent power play came two games ago Nov. 23 against the New York Rangers. … The Penguins and Flyers will play an outdoor game Feb. 23 at Lincoln Financial Field in Philadelphia.
Flyers: Meet Columbus at home on Thursday.
Penguins: Continue a three-game homestand Tuesday against Colorado.