With the score tied 1-1 after the first period, Joni Pitkanen won a battle for the puck along the sideboards in the Tampa Bay end and fed it to Skinner, who weaved through traffic and fired home a wrist shot just 22 seconds into the middle frame.
The Carolina center made it 3-1 10 minutes later, completing an odd-man rush that began when Lightning defenseman Eric Brewer snapped a stick blade at the point.
Teddy Purcell and Brett Connolly found the net for the Lightning.
Tampa Bay's Duane Roloson made 27 saves.
Notable deaths of 2014 [PHOTOS]