Sestito got the game's first goal in the second period -- his first marker since 2010 while a member of the Lighting -- and snapped a 1-1 tie with the decisive score midway through the final frame.
Bryzgalov was working on a shutout until Benoit Pouliot got a shot past him less than 2 minutes before Sestito's game-winner.
The victory was the second straight for the Flyers, who improved to 4-6-0.
Anders Lindback made 22 saves for Tampa Bay, which dropped a second straight.
Reindeer recovered after escaping from Santa during lighting ceremony
Selena Gomez drops F-bomb, walks off stage during Jingle Ball performance