Ovechkin scored his 15th goal of the season on the power play in the first period and added his 16th late in the third, when Carolina came within 3-2.
Both Nylander and Nicklas Backstrom added two assists, while goaltender Olaf Kolzig stopped 35-of-37 shots, as the Capitals won their second straight game under new coach Bruce Boudreau following a five-game losing streak before the firing of Glen Hanlon Thursday.
Goalie John Grahame was beaten four times on 33 shots for the Hurricanes, who have lost four of six.
In man-advantage situations, Washington went 3-for-4 and Carolina went 0-for-3.
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