Jordan Staal, Sebastian Aho and Andrei Svechnikov each had three points for the Hurricanes (32-10-7), who are 5-0-3 in the past eight games. Alex Nedeljkovic made 27 saves.
"We got to the game we wanted to play, everyone was buying in," Staal said. "Everyone was moving their feet and making the right plays. Obviously, it turned into some good stuff."
Dallas is in fifth in the eight-team Central, two points behind the fourth-place Nashville Predators for the final Stanley Cup Playoff berth from the division with two games in hand. Nashville lost to the Florida Panthers 7-4 on Tuesday.
Carolina, Florida and the Tampa Bay Lightning have qualified for the playoffs. The Hurricanes are two points ahead of the Panthers and three ahead of the Lightning for first place.
Jason Robertson scored, and Anton Khudobin made 25 saves for the Stars (21-16-12), who had won six of seven.
"They're big, they're fast, they forecheck and they come at you," Dallas coach Rick Bowness said. "It was more us, our inability to handle all of those issues. We were half a step behind physically and half a step behind emotionally. When you do that against that team, they're going to make you look as bad as we did tonight."