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 2014-15 (also 0-2-2).
"We've got to be better and it starts with me and (Joseph Woll)," Vladar said. "Hopefully we're going to turn this thing around because, obviously, this is not us. This is not fun. Obviously, our game is not at the level it should be."
Mikheyev pushed Tampa Bay's lead to 3-1 at 17:00 of the third period, tucking in a wraparound on the backhand 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.
"We didn't have a ton of real good looks, but I think those shots in traffic are good chances," Point said. "It was a big emphasis after that first game to win puck battles. I think the past two games we have done a good job with that."