Jurrgens allowed nine hits, four runs, walked one and struck out three in five innings.
The Nationals added a run in the seventh when right fielder Jason Heyward dropped a fly by Dunn for a two-base error. Roger Bernadina drove in the run with a sacrifice fly.
Washington got its final run on a solo home run by Ian Desmond, his 10th, in the ninth off Scott Proctor.
“There’s not a whole lot to play for this late. To spoil it for them feels good,” said Desmond.
Heyward reached base four straight times against Hernandez, drawing a pair of walks, a hit by pitch and a single.
NOTES: Dunn’s blast was the sixth longest in Turner Field history. The longest — 471 feet — was by Sammy Sosa on Sept. 1, 2001. … Jurrjens was 6-1 at Turner Field this season in nine starts prior to Tuesday night. … Hernandez had lost two in a row and four of his last five decisions. … It was the 11th time this season the Braves were shutout.