Simon Gagne scored twice short-handed during a four-goal second period that put the Flyers up 4-3, but the Penguins came back to win two nights after they rallied from three goals down in the third period to beat Detroit 7-6 in overtime.
"That was a tough game to play emotionally because of the game in Detroit," Penguins coach Michel Therrien said. "We found a way to get a three-goal lead, but our power play was not very good (1-for-7) and it gave them an opportunity to get back into the game."
Goligoski, the sixth and final Pittsburgh shooter, shifted the puck from backhand to forehand before sliding it along the goal line and into the net behind goalie Martin Biron, who made 27 saves but couldn't preserve the 4-3 lead.
"It's a move I've done before," said Goligoski, a defenseman who has scored three goals. "If something was open to shoot I would have shot, but, yeah, I kind of knew what I was doing."
Biron stopped the more-accomplished Petr Sykora, Kris Letang, Crosby, Evgeni Malkin and Miroslav Satan before Goligoski scored.
"The kid's pretty good at shootouts in practice," Therrien said. "We practice it every week. He definitely has the skill."
Backup goalie Dany Sabourin, who replaced Marc-Andre Fleury to start the third, stopped 11 shots before turning aside Gagne, Mike Richards, Jeff Carter, Kimmo Timonen, Joffrey Lupul and Scott Hartnell in the shootout.
"It's something I practiced during the summer," said Sabourin, who has allowed only one shooter to score in three shootouts this season. "It's something I added to my game."
Malkin scored and set up Crosby's tying goal as the Penguins, winning their fifth in a row, went into overtime for the eighth time in 16 games. They are 6-2, 3-1 in shootouts.
Crosby tied it with 2:33 remaining in the third with his sixth goal and 18th in 22 career games against the Flyers, cutting toward the net from the left circle and scoring when Malkin got the puck out from behind the net.
Crosby and Malkin scored on bad-angle backhanders less than three minutes apart early in the second before the Flyers surged, only to lose their eighth in a row in Pittsburgh - including three Eastern Conference finals games last spring.
"It was 3-0 and we called a timeout," coach John Stevens said. "Exactly what I said was we aren't playing that bad. The three goals that they got we have almost given them. ... The encouraging thing was we were able to come back against a good team."
No matter, the Flyers took the loss harder than most so early in the season, keeping their dressing room door shut for an extended period.
"Late in the (third) period we were doing a lot of good things, and then one mistake against a team that's very opportunistic and it's 4-4," Richards said. "It's a tough way to lose a game."
Carter started the comeback at 7:46 of the second. Barely a minute later, Gagne cut through Goligoski and Malkin on a short-handed breakaway and, with Malkin draped on his shoulder, put a backhander past Fleury.
Gagne tied it at 3 slightly more than five minutes later with his 11th career short-handed goal and second of the period, and Lupul put the Flyers up by deflecting Timonen's shot with four seconds left in the period. Lupul hadn't scored in five games before getting his eighth goal in 14 career games against Pittsburgh.
Notes: Fleury was pulled for the first time since March 6. ... A week ago Thursday, the Penguins led Edmonton by five goals before hanging on to win 5-4. Pittsburgh lost a three-goal lead during a 4-3 loss to Washington on Oct. 16. ... Philadelphia is 0-2 in shootouts. ... The Flyers trailed 2-0 in Pittsburgh on Oct. 14 before losing 3-2 on Pascal Dupuis' overtime goal. ... Penguins F Jordan Staal didn't score after getting three goals in the third period against the Red Wings. ... Theo Fleury set the NHL single-game record with three short-handed goals on March 9, 1991.