Jones drove in two runs and scored three times for the Braves, who have won three straight.
Kyle Davies (3-5), who earned his first win since April 30 against the New York Mets, allowed one run on four hits in five-plus innings with five strikeouts and two walks.
Davies missed more than three months after having surgery on his right groin and was 0-2 in three starts since his return.
Three relievers combined to pitch four scoreless innings and held Washington to just three hits.
Tony Armas (8-12), who has lost his last four decisions, allowed three runs on six hits in 6 2/3 innings.