Brandon Hagel, Anthony Cirelli and Tanner Jeannot also scored, and Jonas Johansson made 27 saves for Tampa Bay (5-2-0).
Eetu Luostarinen had a goal and an assist, and Sergei Bobrovsky made 19 saves for Florida (4-4-0).
Jeannot gave the Lightning a 1-0 lead at 2:37 of the first period.
Ryan Lomberg tied it 1-1 with a short-handed goal at 11:24.
Cirelli put the Lightning back in front 2-1 at 17:01, but Luostarinen scored 32 seconds later to tie it 2-2.
Hagel scored a short-handed goal for Tampa Bay to make it 3-2 at 12:18 of the second period.
Point scored 40 seconds into the third period to extend the lead to 4-2.
