PITTSBURGH — Despite some last-minute heroics to send the game into overtime, the Flyers fell to their bitter rivals Sunday afternoon at reverberating PPG Paints Arena.

And it was their biggest tormentor who helped send them to a 5-4 overtime defeat.

Bryan Rust redirected Sidney Crosby's shot/pass into the net with 2 minutes, 35 seconds left in OT, beating spinning goalie Petr Mrazek to give Pittsburgh the win.

"It was a hard, playoff-type game," Rust said.

Crosby, a certified Flyers killer, had scored 17 seconds into the third period to give the Penguins a 4-3 lead.

With 42.6 seconds left in regulation and the Flyers' goalie pulled for an extra attacker, Sean Couturier tied the score at 4-4 on a rebound of a shot by Shayne Gostisbehere.

"We played a helluva hockey game, and now we have to turn the page and go into Dallas," Flyers coach Dave Hakstol said after his team fired a season-high 45 shots, all in regulation, and limited the Penguins to 32.

"The point is big," center Sean Couturier said. "We needed the two points, but at least we can build on this and move forward."

By salvaging a point, the Flyers moved into a virtual tie for third place in the Metropolitan Division with Columbus. Both teams have 89 points and the same ROW (regulation and overtime wins), and each earned five points in their four-game series. Columbus has the next tie-breaker — a plus-7 goal differential compared to the Flyers' plus-2.

The Flyers are six points ahead of Florida, which is trying to get into the final wild-card spot and has three games in hand.

The Penguins, who scored in the first minute of the second and third periods to take away momentum built by the Flyers, won all four games in the series this season. They swept the Flyers for the first time since 2006-07, when they went 8-0.

Early in the third period, Crosby made a power move to get past  Couturier and, from the left circle, beat a moving Mrazek — who relieved Alex Lyon early in the second period — to the far side to put the Penguins ahead, 4-3.

"I thought he was going to go blocker side because I gave him that, and then I tried to close it, and he put in a wrister on the other side," said Mrazek, who turned aside 19 of 21 shots.

The Flyers had dominated the latter stages of the second period, getting a late goal and the last nine shots of the stanza.

And then Crosby undid all their hard their work by scoring his 38th career goal against the Flyers, the most he has tallied against any NHL team. He has 93 points in 63 career games against the Flyers.

The Penguins made the Flyers pay for Jake Voracek's cross-checking penalty late in the first period.

The penalty carried into the second, and just 37 seconds into that stanza, Patric Hornqvist, left alone in front, beat Lyon with a shot that caromed off the right post and into the net. That tied the game at 2-2.

Just two minutes later, with the Penguins having an extra attacker because of a delayed penalty, Evgeni Malkin's shot appeared to graze off defenseman Andrew MacDonald and through Lyon's legs to give Pittsburgh its first lead at 3-2.

"Maybe if I had a little better focus, I could adjust to that," Lyon said of the deflection.

Lyon, who allowed three goals on 11 shots, was removed from the game after the goal and replaced by the struggling Mrazek.

"It's that time of year, and it felt like we needed a bit of a momentum change," Hakstol said of the goalie switch.

With 2:50 to go in the period, Jordan Weal scored on a rebound while the Flyers were on a power play, knotting the score at 3. It was Weal's first goal in 18 games and it gave him a career-high three points.

"We were able to reset in this building, and it's not an easy building to do that in," Hakstol said. "Our guys stayed with it all the way through the hockey game."

The Flyers' defense got offensive in a first period dominated by the visitors.

Defensemen Travis Sanhem (wrist shot from the high slot) and Brandon Manning (slap shot from above the right circle) scored first-period goals, both set up by perfect drop passes from a patient Weal, to steer the Flyers to a 2-1 lead after the opening 20 minutes — just the 15th time in 76 games they took an advantage into the second period.