Skinner gave Carolina a 2-1 lead in the first period but Nate Thompson tied it with 2:46 to go in the opening stanza. That was all the scoring until Skinner put a wraparound shot past Dustin Tokarski 6:36 into the third.
Chad LaRose scored into an empty net with 22 seconds left in the game.
Cam Ward made 36 saves to get the win, Carolina's second in five games.
Tampa Bay suffered a tough loss against one of the league's weakest teams in its bid to earn a playoff position. Tampa Bay trails eighth-place Washington by seven points.
Tokarski started just his second game in the NHL. He gave up three goals Thursday in an overtime loss to Washington.