Dallas trailed 2-0 in the first period and 2-1 with 2:57 remaining.
Stars forward Jamie Benn tied the game with his second goal of the season when he found the puck, which had been lost in traffic in front of the Pittsburgh crease, and shot it behind a diving Marc-Andre Fleury.
"Crazy is a pretty good word," Seguin said. "We really wanted that game. We thought we had to stay a little bit more disciplined again. It was a tough start. They have a great power play and some very skilled forwards over there. But [goalie Kari] Lehtonen definitely kept us in a certain points in the game and it's nice to come away with a win."
Penguins coach Mike Johnston credited the Stars and admitted Pittsburgh changed the way it played in the third, which allowed Dallas to come back.
"In the third, we came up high along the boards three or four times and they started to push us," Johnston said. "We made plays in those high areas; we've got to make plays either back to the net or inside, but we can't make them up high. Especially later in the game when the ice gets heavier, that type of thing. And we just have to manage the puck better in the offensive zone."
Penguins forward Pascal Dupuis was taken from the ice on a stretcher in the second period. Stars defenseman Alex Goligoski cross-checked Dupuis to the ice with 6:58 remaining in the period. Dupuis took a puck to the head while lying in front of the Dallas crease and immediately shook off his gloves and motioned toward the bench for assistance.
Dupuis was taken from the ice several minutes later and gave the Pittsburgh crowd a thumbs-up as he approached the gate.
Johnston said he was informed Dupuis had some numbness in his arm and that feeling was returning, but did not have any further updates. Players from each team, including Penguins captain Crosby, Seguin, Lehtonen and Goligoski described Dupuis' injury as scary.
"I was looking up at the point to see where the puck was," Goligoski said. "I gave him a little shot and he kind of fell forward. I was kind of looking for the guy off the backside and I think it was [Penguins defenseman Kris] Letang who came in and as he went to shoot, I kind of see [Dupuis] duck down and put his head down.
"I'm not sure where it caught him. Scary moment though."
Stars forward Antoine Roussel made it 2-1, 6:08 into the second. Forward Vernon Fiddler found Roussel in the right faceoff circle from behind the net. Roussel's shot went between Fleury's left arm and the post for his second goal of the season.
Pittsburgh's top-ranked power play (44.4 percent entering Thursday) started strong again, allowing them to build a two-goal lead.
Stars defenseman Brenden Dillon tripped Crosby, whose backhand shot hit the left post, as he charged toward the net. Crosby scored his fourth goal of the season 59 seconds later when he attempted a pass to Chris Kunitz but had the puck deflected by Dallas defenseman Jordie Benn and past Lehtonen 2:28 into the first period.
Forward Evgeni Malkin, who earned the goal's second assist, passed Rick Kehoe for fourth all-time on the Penguins scoring list with 637 points. Malkin trails Mario Lemieux (1,723 points), Jaromir Jagr (1,079) and Crosby (776).
Kunitz scored Pittsburgh's second power-play goal at 7:46 of the first period to extend the lead. Letang slapped a shot off Lehtonen's pad that jumped to Kunitz, who wristed a shot over the goalie's glove for his second goal of the season.
"I think that the first two periods were pretty decent," Crosby said. "I thought in the third, they're down one, they're coming harder. We weren't able to get that next one to generate some chances. We probably made it a little too easy on them, turning the puck over a bit.
"To not even get a point out of that, I think it's a little frustrating."
Lehtonen was unbeatable through the final 52:14, finishing with 27 saves on 29 shots. He was aided by the Stars playing a much cleaner game through the final two periods with no penalties committed after going on the penalty kill four times in the first.
"You need these to be able to build team chemistry and that was huge," Lehtonen said. "We had a horrible start and we hung in there and it was one of those games where they could've put us away in the first and we were able to keep it to only two goals and that made it possible."
The Penguins power play was 6-for-11 on the season following Kunitz's goal before two failed attempts later in the period. Pittsburgh's penalty kill, which entered the game ranked last (54.6 percent), allowed the Stars to control the crease around Fleury in the first, but killed each of Dallas' two power plays.
"I thought we did a real poor job of controlling our emotions," Stars coach Lindy Ruff said. "We took a couple penalties we didn't need to take and they've always had a dangerous power play. They got a little bit of a break on the first power-play goal, but some power plays after that, they were zipping it around pretty good."