Jamie Benn had a goal and an assist while Steve Ott had the other goal for the Stars, who have won four in a row. They've earned points in seven of their last eight games to move into first place in the Pacific, two points ahead of idle Phoenix.
It was Dallas' second win ever in Raleigh.
"The most satisfying thing was that it was a total team effort from us," Dallas coach Marc Crawford said.
Eric Staal scored his third goal in his last four games and Cam Ward stopped 29 shots for Carolina, which was playing its fourth game in six nights. The Hurricanes had earned points in five of their last six games.
"We weren't any good," Carolina coach Paul Maurice said. "We had no jump, no quickness, no pace, missed the net eight times in the first period and were just off."
The Stars' five previous wins were all by one goal, but a strong opening 25 minutes gave Dallas more of a working margin.
The Stars opened the scoring in the first period courtesy of a clever wrist shot by Neal. After a turnover at the Hurricanes' blue line, Loui Eriksson collected the puck behind the Carolina net and fed Neal, who was to Ward's left. Neal quickly snapped the puck above Ward's shoulder.
After Carolina squandered a power play early in the second, the Stars skated ahead on an odd-man opportunity. The Hurricanes had a couple of chances to corral the bouncing puck, but Dallas finally managed to gain control behind the net, and Benn fed Ott for the goal.
Dallas made it 3-0 when Neal ripped a shot from the slot. That attempt went wide, but the puck caromed off the boards and bounded back in front, giving Neal a second chance. His one-timer again beat Ward on the glove side.
"I think tonight we played with more confidence than we had all year," Stars forward Adam Burish said.
Staal brought the Hurricanes within two when he managed to catch up to a loose puck for a breakaway and snapped the puck above Lehtonen.
"We've got to do a better job of trying to get the first goal," Staal said. "We're pretty good at home if we can get that first one and get our crowd going and get our energy up. Tonight was one of those nights where it would have been nice to get that, but it didn't happen."
Otherwise, Carolina looked as though it might be feeling the effects of its heavy workload. The Stars' forecheck caused the Hurricanes to turn the puck over repeatedly, and Carolina had trouble controlling loose pucks.
Benn finished the scoring when he capitalized on an inviting rebound early in the third.
"We're kind of treading water in and around that red line of the playoffs, but we've got to find ways to get above that line," Staal said. "We've got to find ways to win."
Material from wire services and team media was used in this report.
Wrist shot -
1 - 0 DAL
Wrist shot -
2 - 0 DAL