The game was deadlocked at 1-1 heading into the final period and Florida gave itself a chance at victory when David Legwand scored 10:02 into the stanza. Olesz, however, tied it with 6:26 to play and Booth produced the game-winner with 4:12 remaining.
The Panthers won their second straight after losing three in a row.
Scott Clemmensen picked up the win with 27 saves.
Colin Wilson scored Nashville's first goal to create a 1-1 tie midway through the first period. Pekka Rinne gave up three goals on 34 shots to take the loss.