Harper's eighth-inning blast off Josh Edgin (0-1) put the Nationals ahead after John Buck's RBI double in the preceding half-inning had produced a 6-6 deadlock for New York.
Harper finished 3-for-3 with three RBI and three runs scored. Adam LaRoche supplied a three-run home run and Ian Desmond contributed a bases-empty homer for the Nationals, who evened their three-game road set.
Justin Turner and Collin Cowgill each supplied two RBI for the Mets.
Notable deaths of 2014 [PHOTOS]
Arizona Cardinals player formally charged