Jones, 40, was added to the NL All-Star roster before the game. He replaced injured Dodgers outfielder Matt Kemp.
Jones, who plans to retire after this season, went 5 for 5 for his third career five-hit performance and first since Aug. 11, 2002.
After singling in the eighth inning, Jones was lifted for pinch runner Juan Francisco. Jones tipped his helmet as he received an ovation on his way to the dugout. He emerged from the dugout for another wave as the cheers continued.
Jones hit a three-run double in the sixth. He has a season-best 10-game hitting streak and is hitting .313.
Jones added a defensive highlight in the eighth inning when he fielded Darwin Barney’s grounder behind third base and, while in foul territory, threw him out at first.
Jair Jurrjens (2-2) gave up nine hits and three unearned runs in five innings. Reliever Kris Medlen pitched three perfect innings.
The Cubs led 3-1 before Michael Bourn hit a bases-loaded triple in Atlanta’s five-run fifth. Martin Prado’s sacrifice fly and Jason Heyward’s 13th homer in the inning pushed the Braves’ lead to 6-3, chasing Chris Volstad out of the game.
Volstad (0-7) has gone 20 consecutive starts without a win. It is the longest winless streak in the majors since Jo-Jo Reyes made 28 consecutive winless starts for the Braves and the Blue Jays from 2008-11, according to STATS LLC.
Volstad was winless in his last 11 starts with Florida in 2011 and hasn’t won in nine starts over two stints with the Cubs this season.
Bourn walked in the first and scored when Jones’ single dropped in front of David DeJesus in center field. DeJesus dove and trapped the ball.
Cubs relievers Rafael Dolis and Jairo Asencio combined to walk six batters in the sixth, helping the Braves score four runs on only one hit – Jones’ bases-loaded double to right field. Prado forced in a run with a bases-loaded walk from Asencio.
The start of the game was delayed by rain for 52 minutes. After the rain, the first-pitch temperature was 72 degrees, a drop of more than 20 degrees.