It was the Rangers' third straight win and their 12th in 17 games. New York boosted its Atlantic Division lead over second-place Pittsburgh to nine points.
Prust scored his fourth goal of the season 1:57 into the final period for a 3-1 advantage and the Rangers were able to protect it until Jay Harrison put a backhander past Martin Biron with only 40 seconds remaining in regulation.
Artem Anisimov and Brandon Prust had second-period goals for New York and Biron made 21 saves.
Cam Ward allowed the three goals on 25 shots. The Hurricanes fell to 2-1-2 on a six-game homestand.
Celebrity Families of 2014 [PHOTOS]