Whitney's 17th and 18th goals this season came in the third period when Carolina scored three times.
Tampa Bay's lone goal was scored by right wing Martin St. Louis just 23 seconds into the contest.
Karri Ramo allowed two goals on 35 shots in his second NHL start (1-1-0) for the Lightning, who have dropped four of five.
Tampa Bay had won seven of the previous eight meetings between the teams.
On the power play, Carolina went 0 for 3 and Tampa Bay went 0 for 2.