Steve Lombardozzi singled in the go-ahead run 2, in the opener game series.
Wilson Ramos went 2-for-4 and drove in a run for Washington, which has won three of its last four.
R.A. Dickey (8-12) yielded three runs -- two earned -- on eight hits in the loss, New York's third straight. The knuckleballer fanned seven in as many innings.
"As it's happened in so many of his starts, we just didn't give him any runs to work with," Mets manager Terry Collins said.
Washington re-took the lead in the next half-inning, as Lombardozzi singled through the left side with two outs to plate Brian Bixler.
"To get the game-winning RBI is a pretty awesome feeling," said the rookie Lombardozzi, who had been 0-for-15 at the plate prior to the at-bat.
Ramos broke a scoreless tie with an RBI single in the fifth, and Rick Ankiel drove in another run in the sixth.
Nats skipper Davey Johnson managed the Mets from 1984-90, leading them to a World Series title in 1986...Jayson Werth had three of Washington's 10 hits...Detwiler was charged with two runs on three hits and three walks in 5 2/3 innings...Dickey has made 10 straight quality starts, going 4-4 in that span...Three Mets players had double-digit hitting streaks come to an end: Jose Reyes (14), Justin Turner (11) and Bay (10).