McCutchen's clout in the first inning gave the Bucs a quick 2-0 lead and his second shot two innings later doubled the advantage.
Charlie Morton (2-2) earned the decision, yielding three runs on six hits over 6 2/3 innings.
Vin Mazarro entered to record the final out with a runner at second, picking up his first save as the second-place Pirates moved to within 1 1/2 games of St. Louis in the National League Central.
Dan Haren (4-11) was roughed up for five runs on five hits over five full frames for the Nationals.
Werth also clouted a two-run homer in the seventh, logging his second straight two-homer game for Washington.
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