The Flyers lost their third in a row and the Capitals became the last team in the Eastern Conference this season to record a second win.
It was a 1-1 contest heading into the third period, but Troy Brouwer gave Washington the lead 3:57 into the stanza and Wolski extended the advantage with a backhander.
Brayden Schenn brought Philadelphia within one by scoring his first of the season with 9:30 to play, but the Flyers could not get another one past Braden Holtby.
Holtby, who had lost his other two starts this year, made 29 saves. Ilya Bryzgalov stopped 23-of-26 shots for Philadelphia.