Andrej Sekera and Jiri Tlusty also scored for the Hurricanes, who had lost two straight and six of eight before bouncing back to equal their most lopsided victory of the season.
Skinner's two goals and three points both tied career highs. Now in his fourth NHL season, the 21-year-old Toronto native last scored two goals in a game in January 2013, against Buffalo.
Skinner got the only goal of the first period before igniting a three-goal second period with a wrist shot from the left circle. Sekera followed with a power-play goal at 14:09 on a blast from just inside the blue line, interrupting a 3-for-42 stretch by Carolina with the extra man.
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