Sebastian Aho scored his 200th NHL goal for the Hurricanes (30-9-8), who have won three in a row in a six-game point streak (5-0-1).
Antti Raanta made 15 saves in relief of Frederik Andersen, who allowed two goals on six shots before leaving with an upper-body injury after the first period. There was no update after the game.
"The first two periods, we were great," Carolina coach Rod Brind'Amour said. "Just overall, great effort, and then in overtime, nice play by 'Nechy' to win it for us. Overall, I loved the way we competed all night."
Wyatt Johnston and Jason Robertson scored for the Stars (28-13-9), who have lost two in a row but extended their point streak to four games (2-0-2). Jake Oettinger made 21 saves.
"It was pretty tight checking, not a lot of room either way," Dallas coach Peter DeBoer said. "It's always a surprise, as much as you talk about it when you play them, because they're as good as there is in the League at putting that offensive zone pressure on you. But I thought we adjusted to it better as the game went on.
"I think the overtime thing is a bit of a self-fulfilling prophecy right now. We just don't have a lot of confidence for whatever reason in overtime, so we've got to find that swagger again."