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 Division.
"I think tonight we played with more confidence than we had all year," Adam Burish said.
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It was Dallas' second win ever in Raleigh.
The Stars weren't expected to contend for the Pacific Division crown, but Dallas players said back-to-back wins over St. Louis last weekend gave the team a new wealth of confidence.
"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.
"We've done a pretty [darn] good job of staying in the fight, but at some point we have to get above that and get beyond treading water," coach Paul Maurice said of his Hurricanes, who fell below .500.
The Stars' five previous wins were all by one goal, but a strong opening 25 minutes gave Dallas more of a cushion.
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.
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.
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.
"There are no excuses, [including] a tough schedule," Maurice said. "We just weren't any good. We had no jump, no quickness, no pace."
Benn finished the scoring when he capitalized on an inviting rebound early in the third.
"That's a huge boost," Neal said. "It just takes a lot of wind out of their sails."
Dallas is 7-2 against the Eastern Conference. ... Neither team managed a power-play goal even though both teams' penalty killing ranks near the bottom of the NHL. ... Maurice coached in his 1,001st NHL game.
Copyright by STATS LLC and The Associated Press
Arena: PNC Arena Location: Raleigh, North Carolina
Referees: Brad Meier, Kyle Rehman Linesmen: Mike Cvik, Don Henderson
Attendance: 15,382 (82.1% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
James Neal (9)
Assists: Loui Eriksson, Jeff Woywitka
Steve Ott (5)
Assists: Jamie Benn, Trevor Daley
James Neal (10)
Assist: Nicklas Grossmann
Eric Staal (12)
Jamie Benn (6)
Assists: Brenden Morrow, Mike Ribeiro