After losing the first two games of the series, the Braves cooled off the Nationals with a game-changing sixth frame that included home runs from both Dan Uggla and Upton.
Any combination of two Atlanta wins or two Washington losses during the final 10 games of the season will give the Braves the National League East title.
With Washington holding a 2-0 lead, Uggla hit the first pitch of the sixth inning from Ross Ohlendorf (4-1) out to left.
Jordan Schafer then reached on a bunt single and when Ohlendorf threw the ball away at first, Schafer dashed all the way to third.
Two outs later Schafer was still on third, but he came in to score when Upton hit his 26th home run.
Atlanta added runs in the seventh on an RBI double by Brian McCann and in the ninth on a base hit by Schafer that brought home McCann.
Washington lost for just the second time in 12 games.