Jeff Skinner added a pair of goals for the Hurricanes, who finish the season in seventh place in the Metropolitan Division, outside of the playoff picture.
Wayne Simmonds scored twice for the Flyers, who had already wrapped up third place in the Metropolitan Division and a date with the New York Rangers in the first round of the playoffs later this week.
Cal Heeter made 33 saves in his NHL debut for the Flyers, before stopping one of two shots in the shootout.
Hurricanes goaltender Anton Khudobin made 39 saves and stopped all three of shots in the shootout.
