Taylor Raddysh put Tampa Bay ahead 3-0 at 2:56 of the second, and linemate Boris Katchouk poked in a loose puck at the side of the net to make it 4-0 at 6:47.
It was the second straight game with a goal for Raddysh after he scored his first in the NHL on Saturday. Katchouk's goal was his first in the NHL and Colton, who centers the line, had his first multipoint NHL game.
"If we're going to go anywhere, we're going to need that depth scoring," Cooper said. "And now those guys are [scoring] and that's why we're seeing some results. You need those guys to put some pucks in for you."
Mathieu Joseph, who returned to the lineup after missing three games with a lower-body injury, scored shorthanded to make it 5-0 at 8:34. Hart was replaced by Jones after the goal.
Pat Maroon pushed the lead to 6-0 at 5:29 of the third.
Atkinson tipped in a shot by Giroux on the power play to make it 6-1 at 7:04, but Perry scored his own power-play goal at 14:15 for the 7-1 final.
"We'll get back at it here tomorrow (against the Colorado Avalanche)," Flyers coach Alain Vigneault said. "We'll have a couple of quick meetings there, get our guys focused on what we need to do on the ice, and hopefully tomorrow we can bring the energy and a better execution and a better game against a real solid team."
NOTES:The win was the 1,000th in the history of the Lightning, who began play in the NHL in 1992-93. They are 1000-952-154 with 112 ties. ... Tampa Bay defenseman Erik Cernak did not play Sunday and is day to day with a lower-body injury he sustained against the Bruins. ... The Lightning have won 10 straight games against the Flyers. ... Hedman has scored eight points (two goals, six assists) during a four-game point streak. ... The last time the Flyers lost eight straight games (0-6-2) was Dec. 27, 2018 to Jan. 8, 2019.