Tomas Tatar also scored for Detroit, which ended a 12-game regular season losing streak in Philadelphia dating to Jan. 25, 1997. The Red Wings did win the first two games of the 1997 Stanley Cup Final in Philadelphia on their way to a four-game sweep.
Sean Couturier and Claude Giroux scored and Jakub Voracek had a pair of assists for the Flyers.
In the shootout, all three Philadelphia skaters -- Travis Konecny, Giroux and Voracek -- missed.
After Gustav Nyquist and Frans Nielsen misfired for Detroit, Athanasiou beat Steve Mason on the forehand. Athanasiou pumped his fist along the side boards as his teammates came out to congratulate him.
Couturier made it 2-1 off a setup by Voracek 6:51 into the third period. After his wraparound attempt was denied by Jimmy Howard, Voracek sent the puck back in front of the net and Couturier poked it home for his fourth goal of the season but first in 11 games.
Athanasiou tied it with 8:47 left when he raced past the defense before deking around Mason with a forehand shot.
Mason, making his first start since Oct. 29, made 33 saves.
Howard made consecutive starts for the first time this season after making 26 stops in Detroit's 2-1 home loss to the Edmonton Oilers on Sunday. He stopped 23 shots.
The Flyers recorded a 4-3 overtime win over Detroit last Tuesday in Philadelphia in the teams' previous meeting this season.
Giroux gave the Flyers a 1-0 lead with a power-play goal 6 minutes in. Voracek sent a cross-ice pass to Giroux and the Flyers captain went to his knees as he one-timed it high over Howard's left shoulder.
The Red Wings answered just over two minutes later when Tatar netted his second goal of the season after a Flyers miscue. Philadelphia's Brandon Manning attempted to clear the puck from next to his own goal but it was blocked by Henrik Zetterberg, who set up Tatar from behind the net for the point-blank shot.
Notes: Red Wings D Tyler Bertuzzi made his NHL debut in place of Thomas Vanek, who missed his seventh game with a lower body injury. Vanek is on longterm IR and is out until at least Nov. 20. Bertuzzi is the nephew of former NHL player Todd Bertuzzi. ... Flyers F Wayne Simmonds got a knockout of Jonathan Ericsson with a left hook during a second-period fight. ... The teams wrap their three-game season series on Dec. 11 in Detroit. ... Konecny delivered big second-period hits to Justin Abdelkader and Steve Ott.