Roberto Luongo made 30 saves for the Panthers (0-3-2).
The Lightning went ahead 2-0 in the third period when Vladislav Namestnikov passed across to Kucherov in the right circle. His wrist shot got past Luongo on the stick side with 12:07 left. Kucherov added an empty-net goal with 1:10 left, also with an assist by Namestnikov.
Kucherov leads the Lightning with five preseason goals and Namestnikov now has a team-leading seven assists.
The Lightning went ahead 1-0 just 2:43 into the game when Palat backhanded the puck got past Luongo's glove from the right side.