The Lightning have now won five of their last six games.
Andrei Vasilevskiy made 29 saves.
Killorn tied the game at two off a rebound of a Slater Koekkoek slap shot at 13:28.
Philadelphia took a 2-1 lead at 19:05 of the second period when defenseman Ivan Provorov scored his first NHL goal on a wrister that eluded Vasilevskiy.
Tampa Bay took a 1-0 lead at 19:57 of the first period when Victor Hedman scored a power-play goal. Hedman took a slap shot from the right side of the point that beat Mason on the glove side.
The Flyers tied the game 1-1 at 6:06 of the second period when Dale Weise scored his second goal in the past two games. Weise sent a shot on goal that Vasilevskiy appeared to make a save on but the puck bounced off his glove and into the net.
Nikita Kucherov scored his tenth goal of the season with 1:15 remaining in the third period to make it 4-2.
The Bolts host the Columbus Blue Jackets on Friday at Amalie Arena. Happy Thanksgiving!