Brandon Hagel and Jake Guentzel also each had a goal and an assist, Brayden Point and Pontus Holmberg scored, and Jonas Johansson made 20 saves for Tampa Bay (28-13-3), which won 7-2 at Xfinity Mobile Arena on Saturday.
Point left the game at 4:29 of the second period. On the scoring play, Flyers defenseman Cam York fell on Point's right leg, and the forward was helped off the ice and did not return.
The winning streak matches the Colorado Avalanche (twice) and the Buffalo Sabres for the longest in the NHL this season.
Christian Dvorak scored and Dan Vladar made 21 saves for Philadelphia (22-14-8), which has lost its third straight game (0-2-1).
Holmberg gave the Lightning a 1-0 lead at 1:10 of the first period when he knocked a loose puck in the slot past a heavily-screened Vladar five-hole.
The Lightning went ahead 2-0, 33 seconds into the second period when Guentzel redirected Erik Cernak's one-timer from the left point.
Point extended Tampa Bay's lead 3-0 at 4:29 with a power-play goal, getting the rebound of an Oliver Bjorkstrand shot and putting it in with a backhand shot in front.
Dvorak made it 3-1 at 5:40 when he kept the puck on a 2-on-1 rush with defenseman Nick Seeler and scored on a wrist shot from the right face-off circle.
Hagel put the Lightning ahead 4-1 at 19:29 with a power-play goal from the left face-off circle.
Kucherov scored an empty-net goal at 16:39 of the third period for the 5-1 final.
The win marked the 600th for Lightning coach Jon Cooper. He's the 25th NHL coach to reach that milestone, and the third to do it with one team, along with Al Arbour of the New York Islanders (740) and Lindy Ruff of the Buffalo Sabres (631).
