Atlanta scored five times in the final two innings to come back from a 5-1 deficit and win its second straight game.
The Braves closed within one thanks to a three-run eighth that included an RBI single from Dan Uggla and a two-run base hit by Ramiro Pena.
Carlos Marmol (0-1) then came on for the Cubs in the ninth in hopes of preserving the lead, but B.J. Upton led off with a homer to center on a 3-1 pitch. After Jason Heyward hit a hard liner to left for an out, Justin Upton it a 1-2 pitch over the center-field wall for the game-winner.
It was Justin Upton's second blast of the game following his solo shot in the first.
Eric O'Flaherty (1-0) picked up the win by pitching a scoreless top of the ninth.