With the Hurricanes clinging to a 2-1 lead, Carolina's Eric Staal picked up a loose puck in his own end and skated in alone on goalie Ben Scrivens, who made the initial save.
But Skinner was there for the rebound and put it in the net for the Hurricanes, who logged just their third win in 10 games.
Phil Kessel got both goals for Toronto -- giving him an NHL-leading 14 for the year -- including a tally with 1 minute remaining.
Scrivens ended with 38 shots as the Leafs lost for the fourth time in five games.
2014: The Year in Music [PHOTOS]