Toronto fought back to take a 3-2 lead into the third period and then piled on three more goals against Scott Clemmensen to win for the eighth time in 10 games.
Franson scored with 3:11 to go in the first period, cutting the Maple Leafs' deficit to 2-1.
Toronto then stunned the Panthers with two goals in the opening minute of the second period to take the lead. Mason Raymond tied the game 27 seconds into the middle period and James van Riemsdyk produced a power-play goal on a deflection 31 seconds later.
Jonathan Bernier recovered from a shaky start to get the win with 35 saves. Clemmensen gave up all six goals on 32 shots.