The hit by Gonzalez, his second of the game, broke a 1-1 tie with two outs in the top of the 15th against losing pitcher Boone Logan (1-1).
Adam Dunn's 105th RBI of the season came on a seventh-inning single, while Ian Desmond added two hits for the Nationals, who -- despite having baseball's worst record (59-103) -- finished the 2009 season with a record seven-game winning streak in their longest contest since they relocated from Montreal in 2005.
The winner was Logan Kensing (1-2).
Nate McLouth produced Atlanta's only run with a sixth-inning solo homer, his 20th this season.
Omar Infante had three hits, while Yunel Escobar and Martin Prado had two hits each for the Braves, who lost their final six games.
Celebrity Families of 2014 [PHOTOS]