"We were losing every single race to the puck. Execution wasn't there," center Jordan Staal said. "There were other things we could have done and had a better start if we were going to win that one."
Dallas took a 3-0 lead at 5:24 of the second period when Seguin scored his sixth goal on a breakaway after leaving the penalty box.
Pitlick scored his second goal off a pass from Antoine Roussel at 7:46 of the second to push the Stars lead to 4-0.
"The second goal, [Roussel] made a heck of a playing getting in on the forecheck, got the puck, put it right on my tape, and I just shot it and I shot it hard," Pitlick said.
Skinner cut the Dallas lead to 4-1 when he scored on his own rebound with 10 seconds left in the period. He made it 4-2 with his fifth goal at 5:32 of the third period.
"He's been doing this for a long time," Hurricanes coach Bill Peters said. "He gets the puck, he works hard, so he's getting rewarded for that right now."
Stars coach Ken Hitchcock challenged the second Skinner goal, claiming he interfered with Bishop before scoring, but it was upheld after video review.
Staal scored to make it 4-3 at 15:24 of the third, three seconds after Stars forward Remi Elie exited the penalty box after being called for delay of game.
Darling made 22 saves.