Morrison, who was claimed off waivers from Anaheim last week, scored the last of three second-period Dallas goals to give the Stars a 3-1 advantage.
Ray Whitney brought the Hurricanes within one with 6:15 to play, but Turco was perfect the rest of the way to halt Carolina's point streak at five games (4
Cam Ward, making his 17th consecutive start in goal, stopped 28 shots for Carolina.
The Hurricanes have not won in Dallas since Feb. 11, 1996, when they were the Hartford Whalers.
2014: The Year in Music [PHOTOS]