In the first post-season game of his NHL career, Ovechkin scored unassisted with 4:32 to play, thus extending the late regular-season momentum that carried the Caps into the playoffs.
Washington won its final seven games of the regular campaign and 11 of its last 12. Ovechkin, the league's leading scorer, produced 30 points in Washington's last 18 games.
The sixth-seeded Flyers owned a 4-2 lead going into the final period, but Mike Green scored twice in the first 6:26 of the stanza to tie it. The second of Green's goals came on the power play with Ovechkin recording an assist.
With overtime looming, Ovechkin came in alone on Philadelphia goaltender Martin Biron and lifted the puck just under the crossbar.
Philadelphia scored three unanswered goals in the second period to take its 4-2 lead. Two of those goals came from Daniel Briere.
Washington will host the second game of the series Sunday.