Michael Bourn reached on a leadoff single and Kerry Wood issued two walks before Uggla drove a 1-1 pitch back up the middle for his third hit of the game. Freddie Freeman helped set up the big inning by hustling down the line to prevent a potential double play.
Wood (0-2) has struggled since he was sidelined for three weeks with right shoulder fatigue, yielding two runs in each of his two outings since he was activated from the disabled list on Thursday.
Kris Medlen (1-0) pitched a perfect seventh, Jonny Venters worked out of a jam in the eighth and Craig Kimbrel finished for his 10th save.
The Cubs wasted another effective outing by Ryan Dempster, who struck out seven in seven innings. The right-hander yielded only one run and six hits, but remained winless on the year and his ERA actually increased from 0.95 to 1.02.
Atlanta put at least one runner on in five of Dempster’s innings, but struggled to score for the second game. Freeman was particularly unlucky, hitting a liner right at shortstop Starlin Castro with a runner on in the fourth and another rocket right to Dempster in the sixth.
The Braves finally got on the board in the fifth. Jason Heyward led off with a drive into the right-field corner for his third triple of the season, then scored on Tyler Pastornicky’s sacrifice fly.
It was the second run in 15 innings for Atlanta, which lost 5-1 in the series opener on Monday night.
Randall Delgado left after Alfonso Soriano’s two-out RBI double in the sixth. But it was still his second consecutive solid outing. The Braves right-hander allowed three hits and struck out five.