Trailing 3-2 entering the sixth inning, the Mets erupted for four runs to grab control of the contest.
After Todd Coffey came in to pitch, Harris lined the first pitch he saw down the left field line for a Mets lead.
Ryota Igarashi (3-1) earned the win after working out of a bases-loaded, two-out jam in the fifth. Josh Stinson and Jason Isringhausen combined for three scoreless frames and Bobby Parnell picked up his fifth save for the Mets.
Hernandez went 5 1/3 innings, yielding six runs on eight hits for the Nats, who dropped the rubber match of a three-game set.
Danny Espinoza went 3-for-3 with a run scored and an RBI in the loss.