Michael Bourn singled and Martin Prado walked to lead off the eighth against Kerry Wood (0-2), and each advanced on Freddie Freeman's groundout. After Brian McCann drew a walk to load the bases, Uggla grounded a 1-1 pitch to the left of second base, chasing home the two decisive runs.
Kris Medlen (1-0) pitched a scoreless seventh inning to earn the victory, and Craig Kimbrel collected his National League-leading 10th save as the Braves evened their three-game set with the Cubs.
Chicago starter Ryan Dempster held Atlanta to one run on six hits over seven frames but finished with a no-decision.
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