Playing without star forward Alex Ovechkin for the first time this season, the Capitals took an early three-goal lead and seemed on their way to tying Philadelphia for the top spot.
But the Flyers scored four straight and earned a point by going into overtime.
Philadelphia has two more games remaining (10-8).
Semin beat Brian Boucher with a nifty move and backhanded a shot into the top corner for the winner.
Ville Leino scored on the first shot, and Matt Hendricks answered for the Capitals.