Neal scored at 1:03 of the extra session to lift the Penguins past the Hurricanes 4-3 on Friday night.
The Eastern Conference leaders rallied from one goal down in the third period and took a 3-2 lead -- only to let it slip away late in regulation before Neal's goal in OT gave them their 13th win in 15 games.
"That's where our team has matured and changed, and I think we regrouped and didn't let it bother us," Neal said. "We come right back and get one."
"When we got our third one, I felt pretty good about it," goalie Marc-Andre Fleury said. "Disappointed to give up that third goal, but it was nice to see (Neal) finish it up for us."
Fleury stopped 31 shots in his 500th career game.
"Marc was our best player tonight, for sure," coach Dan Bylsma said.
They let a third-period lead slip away for the second straight game. Carolina also lost its seventh in eight games with four coming in overtime, and fell 20 points behind the Penguins.
"When you look back, you feel like you had a really good hockey game," Carolina coach Kirk Muller said.
"It's during those first 60 minutes, we had some opportunities to capitalize, and when you don't, you're going to be in tight games and you've got to know how to play with the lead then. It's a very thin line of winning and losing. When you give up a couple of chances and they score, that's the difference."
Engelland -- who was playing in his first game since serving a five-game suspension for a check to the head of Detroit's Justin Abdelkader -- put a hard shot past Peters with 6:45 left to give the Penguins a 3-2 lead. But Bowman forced overtime when he slipped his late wraparound past Fleury.
Engelland was one of a few Penguins making their return to the ice. They also got defenseman Brooks Orpik and forward Tanner Glass back from injuries. Orpik missed eight games with a concussion while Glass was out for the past month with a broken hand.
The Penguins tied it at 2 at 1:58 of the third period when Conner slipped a backhand past Peters.
That came after Carolina built a 2-1 lead following a wild end to the first period and start to the second.
Sekera scored the game's first goal in the final moments of the first period, beating both Fleury and the buzzer with a high backhand that was upheld by a brief review that determined that there were 1.3 seconds left.
That came about a minute after the Penguins had a goal disallowed because the whistle blew before the puck crossed the line during a pile-up in front of Peters and defenseman Ron Hainsey.
Crosby then tied it 16 seconds into the second when he slipped a backhand past Peters for his NHL-best 55th point. But the tie didn't last long -- Gerbe put Carolina back up 14 seconds later by converting on Alexander Semin's hard shot.
"You can't be afraid to have the lead and play," Muller said. "You've got to keep playing the way you played the first two periods. You can't sit back. That's what we tried to emphasize."
Penguins C Evgeni Malkin (lower-body injury) missed his sixth straight game, though he did take part in the team's morning skate. ... The Hurricanes activated G Anton Khudobin from injured reserve and assigned him to their AHL affiliate in Charlotte, and placed D Jay Harrison on IR with a concussion. ... Pittsburgh RW Pascal Dupuis will have surgery on his right anterior cruciate ligament and could miss the season, coach Dan Bylsma said before the game.