Brayden Point and Brandon Hagel scored, and Nikita Kucherov had two assists for the Lightning (2-1-0), who have won two straight after losing their season opener 5-1 to the New York Rangers. Andrei Vasilevskiy made 13 saves.
Dan Vladar made 32 saves and Tyson Foerster scored for the Flyers (0-2-2), who opened the season with four straight losses for the first time since 2014.
Mikheyev pushed Tampa Bay's lead to 3-1 at 17:00 in the third period when he tucked in a wraparound after taking a pass from Holmberg. It was his first goal with Tampa Bay after signing a four-year, $15.4 million contract ($3.85 million average annual value) as a free agent on July 1.
Hagel scored an empty-net goal at 19:53 for the 4-1 final.
Point gave Tampa Bay a 1-0 lead at 16:05 of the first period, scoring on a redirection from below the hash marks after John Carlson sent the puck to the net.
Holmberg extended the Lightning lead 17 seconds into the second period, making it 2-0 on a shot from the right circle on the rush that beat Vladar high on the glove side.
Foerster scored for Philadelphia to make it 2-1 at 7:22 when he sent the puck to the net and deflected off of Charle Edouard D'Astous' stick and past Vasilevskiy.
