Harvey (4-0) allowed the lone Washington run on four hits and struck out seven. The Mets had lost at home to the Nationals eight straight times.
Ike Davis and Lucas Duda both hit two home runs in support of Harvey. Davis had a solo shot in the sixth and a two-run blast in the eighth. Duda's homers were solo affairs, also coming in the sixth and eighth.
Stephen Strasburg (1-3) was unable to match Harvey, giving up four runs over six innings.
Washington suffered its fifth loss in seven games while the Mets ended a three-game skid.