Nino Niederreiter scored twice, and Brady Skjei had two assists for the Hurricanes (42-15-7), who have lost five of six. Frederik Andersen made 12 saves.
"I don't know if I've seen a better game in 20 years of being here," Carolina coach Rod Brind'Amour said. "As far as doing everything we were trying to do, we just didn't get it in the net as much as we would like."
Jamie Benn gave the Stars a 1-0 lead 30 seconds into the second period when his centering pass deflected into the net off the stick of Hurricanes defenseman Ian Cole.
Niederreiter tied it 1-1 from the slot at 6:44 after Skjei intercepted a pass and fed him.
Vincent Trocheck put the Hurricanes ahead 2-1 with a power-play goal at 2:43 of the third period. Wedgewood stopped Aho's shot from the slot, but Trocheck scored on the rebound at the top of the crease.
Hintz tied it 2-2 at 3:43 from between the circles off a pass from Pavelski.
"I knew if I just beat the guy through the middle, he's going to find me," Hintz said of Pavelski. "There were two times that happened today, and it's nice that he sees it so well."