The Mets overwhelmed the Nationals in the opener 11-0, but came up short when New York's Matt Harvey engaged Washington's Ross Ohlendorf in a pitcher's duel during the second contest.
The game had been tied since the fifth when LaTroy Hawkins (3-2) came on in the ninth in a bid to get the Mets into extra innings.
He retired the first man he faced, but Zimmerman then sent a 3-1 pitch over the wall in right for his 12th home run.
That made a winner out of Rafael Soriano (2-2), who escaped a jam in the top of the ninth after putting two runners on base.
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