Panthers snapped a three-game losing streak after rebounding from a 2-0 deficit midway through the game. Radek Dvorak, Dmitry Kulikov and Shawn Matthias scored three straight goals to give Florida a 3-2 lead 8:31 into the final period.
But Sean Bergenheim tied the score at 3-3 with less than 6 minutes left to force a scoreless overtime and then the shootout.
Tomas Vokoun allowed three goals on 37 shots but came up big in the shootout, stopping Martin St. Louis's bid to extend the contest with a tough wrist shot.
Teddy Purcell and Dana Tyrell gave Tampa Bay an early lead but it wasn't enough for the win.
Dan Ellis allowed three goals on 27 shots for the Bolts.