Stamkos made it 2-0 at 6:43 of the second period when he stuffed in a rebound off his own shot from down low.
"I thought our first period was competitive," Flyers coach Alain Vigneault said. "Unfortunately, they sneaked one through there right off the hop. Our guys battled hard, but in the second their power play definitely gave them momentum.
"For the last 30 minutes of the game we weren't very good. Our passing game was off, it created numerous Grade-A opportunities for them. They were the better team."
Perry extended the lead to 3-0 at 16:17 when he went top shelf with a wrist shot with the Lightning having an extra attacker because of a delayed penalty call.
It was his first goal in 38 games, since April 7, 2021 against the Toronto Maple Leafs while he was with the Montreal Canadiens. Perry signed a two-year contract with the Lightning on July 29.
"It was a tough start," Perry said. "Things were going in during preseason, but that doesn't matter. It's all about what you do in the regular season and continue to do down the road."
Alex Barre-Boulet made it 4-0 at 7:26 of the third period with a shot outside the right circle.
Barre-Boulet has scored in consecutive games since being called up Sunday to replace injured forward Brayden Point in the lineup.
"We've dealt with this kind of stuff before," Stamkos said. "Our depth has always been key to our success. A lot of people have been talking about the guys that left, but we've got some really good players that came in, including the young guys who have stepped up."
NOTES: Flyers center Derick Brassard left midway through the first period with a lower-body injury. There was no further update. ... Bogosian had his first multipoint game since March 7, 2019. ... Stamkos has scored 493 points (238 goals, 255 assists) in 434 home games, surpassing Martin St. Louis for the most in Lightning history. St. Louis scored 491 points (193 goals, 298 assists) in 480 home games. … Stamkos has 80 three-point games in the NHL. Only six active players have more (Sidney Crosby, 151; Alex Ovechkin, 120; Joe Thornton, 112; Evgeni Malkin, 101; Patrick Kane, 94; Nicklas Backstrom, 83). … Only three goalies have more shutouts than Vasilevskiy since he entered the NHL in 2014-15: Marc-Andre Fleury (40), Tuukka Rask (29), Pekka Rinne (28). … Lightning defenseman Mikhail Sergachev had two assists. … Philadelphia forward Oskar Lindblom played his 200th NHL game. … The Flyers were playing the first of a back to back. They play at the Florida Panthers on Wednesday.