The Nationals were trailing 4-3 entering the seventh inning but exploded for five runs to grab control of the contest.
Steve Lombardozzi began the rally with a leadoff walk off Jake Diekman (0-3), went to second on Denard Span's sacrifice and stole third. After Ryan Zimmerman walked, Lombardozzi came home with the tying run on Bryce Harper's RBI groundout.
Zach Miner then took the mound and Werth (3-for-5, three RBI, three runs scored) greeted him by poking a pitch just inside the left field foul pole for his 1,000th career hit -- a two-run homer.
Anthony Rendon later capped the rally with a two-run single as Washington clinched its three-game series.
Rookie Tanner Roark (1-0) earned the win in his second major-league appearance and Rafael Soriano picked up his 29th save for Washington.
Darin Ruf bashed a two-run homer and Domonic Brown added a solo shot for the Phillies.