After James van Riemsdyk pulled the Flyers within a goal, Point answered back with less than three minutes to play in the period to give the Bolts a 3-1 lead through 40.
Johnson and Point then scored power play goals 11 seconds apart midway through the third to give the Lightning a four-goal advantage.
It wouldn't be enough.
Helped out by a series of Lightning penalties, Philadelphia scored four goals in six minutes to level the score and even came close to taking the lead. Louis Domingue faced a flurry of action as the Flyers pushed for the game-winner and had to make a key stop on a Dale Weise breakaway late in the game.
After hanging on to force overtime, Anthony Cirelli scored the game-winning goal 1:47 into the extra frame. Cirelli fought to win a puck battle behind the Flyers goal then stepped out in front and beat Philaelphia goaltender Calvin Pickard to give the Lightning both points.
For the second straight game, the Lightning struggled killing penalties. After going 3-for-5 on the kill on Saturday Tampa Bay has now allowed five power play goals in its last two games.
Despite the final scoreline, Louis Domingue was solid in net, making 40 saves on the afternoon, including some critical stops down the stretch as the Flyers had all of the momentum. He also picked up the second assist of his career, notching a helper on Erne's game-opening goal.
