Isaac Ratcliffe, Travis Sanheim and Scott Laughton scored, and Carter Hart made 28 saves for Philadelphia (15-23-8), which had won two in a row.
"It's not like one part of our game broke us down tonight," Flyers coach Mike Yeo said. "You can start with 1-on-1 battles, loose puck races, you can move into execution, you can move into the structure, the details of our game.
"We've started to try to establish what our standards are in certain areas and today we didn't meet those standards."
It was the opener of a home-and-home; the teams play again at Detroit on Saturday.
Larkin's power-play goal put the Red Wings ahead 1-0 at 2:43 of the first period. His shot from the right face-off circle went in off the skate of Flyers defenseman Ivan Provorov.
Ratcliffe tied it 1-1 20 seconds later with his first NHL goal at 3:03. Zack MacEwen's shot from the high slot went in off Ratcliffe.
The goal, in Ratcliffe's third game, was upheld after the Red Wings challenged for goaltender interference.
"I drew it up a million times in my head how I was going to get my first NHL goal since I was young," Ratcliffe said. "I don't think any of the times I drew it up, it was going to go off my pants and in, but I'll take what I can get."