Philadelphia won three out of four in the series and has captured six of its last eight contests.
The teams battled to a 1-1 tie through six innings, but Darin Ruf opened the Philadelphia seventh with a double off Washington starter Jordan Zimmermann (12-4).
Kyle Kendrick (8-6) gave up a run on five hits over seven innings to collect the win. Kendrick had given up a combined 10 runs and 22 hits in his previous two starts.
Jonathan Papelbon struck out one in a perfect ninth for his 20th save.