Skinner and Jussi Jokinen scored in regulation and Ward turned aside 38-of-40 shots for the Hurricanes, who pulled to within three points of Buffalo for the eighth and final Eastern Conference post-season spot.
Alexander Semin and Marcus Johansson scored for Washington, which fell three points behind Philadelphia in the race for the East's top seed with five games to play.
Varlamov stopped 24 shots for the Caps.
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