The Nationals captured the last three games of the four-game series, overcoming a three-run Chicago ninth that brought about extra innings.
Denard Span opened the Washington 13th with a double and was sacrificed to third by Steve Lombardozzi.
Tracy then hit for pitcher Craig Stammen and with a 2-2 count barely made contact on an offering from Michael Bowden (1-3).
The ball bounced slowly down the line, giving Span plenty of time to score what turned out to be the winning run. Bowden made an excellent fielding play just to record an out at first.
Stammen (7-5) picked up the win with two innings of hitless relief and Drew Storen needed just eight pitches to get through the bottom of the 13th for his third save.
Washington took a 4-0 lead into the eighth, but Chicago got one run back in that inning on a home run by Brian Bogusevic and the Cubs struck for three more in the ninth, the final two scoring on Donnie Murphy's homer.