Jones had two runs, three hits and two RBI; Jeff Francoeur hit a two-run triple; and Adam LaRoche hit a sacrifice fly for the Braves (51-59), who averted a three-game sweep by snapping a three-game losing streak.
The winner was reliever Macay McBride (3-1). Bob Wickman recorded his fifth save for the Braves.
Atlanta revoked waivers on Jones, who had been claimed by an unidentified team.
"It was just business," said Manager Bobby Cox.
The losing pitcher was reliever Gary Majewski (4-4).
Cincinnati shortstop Royce Clayton played in his 2,000th career game.
Swim Week Miami Beach 2014 [PHOTOS]