Stamkos' score came 5 1/2 minutes into the final frame and proved to be decisive as the Lightning recorded just their second win in nine contests.
Anders Lindback was busy in net, turning aside 37-of-39 shots.
The Panthers not only dropped a fourth straight but also lost Kris Versteeg, who left in the third period with an injured knee after a collision with the Bolts' Radko Gudas.
The injury came after Versteeg had scored in the second period.
Tomas Kopecky also scored and Jacob Markstrom yielded three goals on 13 shots for Florida.