The Panthers were handed the chance to put themselves in the lead when Buccaneers quarterback Winston fumbled the snap in wet conditions, and the visitors drove towards the endzone.
The hosts' defense made the stand to force the field-goal attempt from Graham Gano, but the kicker had no problem sending his effort through the posts.
Carolina extended their advantage when Winston committed his second turnover of the game as he was picked off by Josh Norman, who returned the ball for a 46-yard touchdown.
Tampa Bay got back into the match when Winston rallied his side and drove them inside the five-yard line before he handed the ball off to Doug Martin, who ran over the right side of the line for the touchdown.
The Buccaneers had the chance to close the gap to four points before the break with a 29-yard field goal, but Kyle Brindza put his kick wide of the posts.