Gio Gonzalez (16-6) pitched into the sixth inning, allowing one run and seven hits, and the Nationals won for the third time in their past four games.
Washington (75-46) has the best record in the majors and a five-game lead in the National League East over the Atlanta Braves, who lost 5-0 to the Dodgers on Sunday. The Nationals host the Braves in a three-game series starting Monday.
Tyler Clippard pitched a perfect ninth for his 27th save in 31 chances.
Jeremy Hefner (2-5) gave up five runs and eight hits as the Mets lost for the ninth time in 13 games.
Michael Morse led off the second inning with a single. With one out, Espinosa hit his 14th home run into the left-field visitors' bullpen to give the Nationals a 2-0 lead.
Washington got another pair of runs with three straight hits an inning later. Jayson Werth led off with a single, Harper followed with a run-scoring triple and scored on Ryan Zimmerman's single.
It was Harper's team-leading sixth triple, and the 19-year-old added another run when he led off the fifth with his 12th homer off the front of the upper deck in right-center field, giving Washington a 5-0 lead.
Gonzalez wasn't particularly efficient, throwing 110 pitches in 5 2-3 innings, but he kept the Mets off the scoreboard until the sixth, when Ike Davis led off with a double and scored on Jason Bay's groundout.
New York had other scoring opportunities but didn't capitalize. Ronny Cedeno led off the fourth inning with a triple but was left stranded at third.
In the seventh, the Mets had runners on first and third with one out before reliever Craig Stammen got Scott Hairston to ground into a double play to get out of the jam.
New York added another run in the eighth inning off reliever Michael Gonzalez. Cedeno doubled with one out, moved to third on a groundout and scored on Kelly Shoppach's single.
The Mets were 1 for 11 with runners in scoring position.
NOTES: Rain delayed the start of the game 2 hours and 26 minutes. ... Mets pinch-hitter Daniel Murphy was ejected after being called out on strikes to end the eighth inning. ... Nationals SS Ian Desmond was in the starting lineup even though manager Davey Johnson had said Saturday he would give Desmond the day off. Desmond went 0 for 4. ... New York opens a four-game home series with Colorado on Monday. RHP R.A. Dickey (15-4) faces the Rockies' RHP Alex White (2-6). ... Washington RHP Jordan Zimmermann (9-7) will start Monday against Atlanta RHP Tim Hudson (12-4).
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