New York tied the game at 2-2 in the eighth and relievers from both sides teamed to give up just eight hits over the next six innings.
After Easley singled off Hanrahan (0-1) to open the 14th, Jose Reyes popped out. Easley then moved up on an errant pickoff attempt, but Ryan Church struck out to give the Nationals a chance to get out of the inning.
Hanrahan's first pitch to Schneider bounced in front of the plate and over the shoulder of catcher Wil Nieves.
That made a winner out of Jorge Sosa (2-1), the seventh New York pitcher, who worked two innings.
The Mets swept the three-game series from the Nationals.