With the game tied 2-2 in eighth, Upton came up to lead off the inning and lined a 3-2 pitch from Tyler Clippard (6-2) just over the fence in the left field corner for his fourth homer in five games.
Freddie Freeman went 3-for-4 with a pair of runs-scoring singles for National League East-leading Atlanta, which extended its lead over second-place Washington to 13 1/2 games with a victory in the first of a three-game series.
David Carpenter (3-0) earned the decision with 1 2/3 scoreless relief innings and Jordan Walden nailed down the victory with his first save for the Braves.
Adam LaRoche and Anthony Rendon each had two hits with an RBI for the Nationals.
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