Philadelphia had scored three straight goals — including two in the third period — to erase a two-goal deficit.
John Carlson and Joel Ward both scored from point-blank range on Philadelphia's Ray Emery in the second period to give the Capitals a 2-0 edge. Emery finished with 29 saves on 32 shots.
Jakub Voracek started the Flyers' comeback, taking a pass from Jason Akeson and scoring on David Leggio to make it 2-1 in the final minute of the second period. Vincent Lecavalier tied it with a power-play goal 1:53 into the third, and Akeson put Philadelphia in front at 6:09.
Leggio stopped 14 of 17 shots in relief of Michal Neuvirth, who turned aside all 16 shots he faced.