Killorn gave the Lightning a 4-1 lead at 10:49 when he caught Hart out of position and stuffed the puck in from the right circle.
Lemieux cut it to 4-2 at 12:40 with his first goal of the season, a redirection from Cam York.
After Flyers defenseman Tony DeAngelo received a five-minute major penalty for spearing Lightning forward Corey Perry, Kucherov scored on the power play again at 17:38 with a backhand for the 5-2 final.
DeAngelo was also given a game misconduct.
"What was it, 3-0 on the power play? 5-2 game, there's the game," DeAngelo said. "That's what they do to teams, and they did it to us. That's the way it goes; you've got to find a way to kill it."
NOTES:Tampa Bay defenseman Victor Hedman did not play (undisclosed) and is day to day. He was replaced by defenseman Erik Cernak, who was plus-1 in 20:55 of ice time after missing two games with a lower-body injury. … Kucherov extended his Lightning record home point streak to 22 games (39 points; seven goals, 32 assists). ... Killorn has six points (four goals, two assists) in the past four games. ... Sergachev reached 40 points for the first time since his rookie season (2017-18). … Philadelphia forward Owen Tippett had an assist and a game-high nine shots on goal in 23:47.