Niese (6-2) held the Nationals to only one run over seven innings, allowing six hits, walking none and striking out eight. Niese hasn't lost since a May 16 setback to Florida.
Francisco Rodriguez survived a shaky ninth inning, allowing run-scoring singles to Roger Bernadina and Ian Desmond before finally picking Bernadina off at third base to end the game and rack up his 19th save.
Cora's triple in the fourth inning put the Mets up 4-1 and Niese chased him home with a double for another New York run.
Josh Willingham homered for the Nationals. Starter Luis Atilano allowed all five Mets runs and lasted only 3 2/3 innings.