"When things are going bad, you don't get breaks," Wood said. "I didn't get any tonight."
Michael Bourn reached on a leadoff single and 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.
"I was just trying to get something in the air towards the middle of the field and it ended up finding a hole," Uggla said. "That's what we needed."
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.
"Shoulder's great, that's the frustrating thing," he said. "I bounced back from the injection and shoulder feels great. I actually threw some good curveballs tonight for the first time in a while. It's all about results, it didn't happen tonight."
Wood cut short the postgame interview when asked about throwing his hat and glove into the stands.
"It's frustrating," Cubs manager Dale Sveum said. "It doesn't matter if you're young or a veteran guy. You give up a couple runs and walk a couple guys, it's frustrating, no matter how many years you have in the big leagues. It's frustrating to do that in a tie ballgame."
Chicago wasted another effective outing by Ryan Dempster, who struck out seven in seven innings. The right-hander yielded just one run and six hits, but remained winless on the year and his ERA actually increased a tick, from 0.95 to 1.02.
"I just try to execute my pitches and control the innings," he said. "The other stuff you can't worry about. You can only control one thing when you're on the mound and that's trying to put the ball where you want to put it. If you do that, more often than not, you'll get good results. The more good results you get, the more wins you'll get."
Braves starter Randall Delgado allowed one run and three hits in 5 2-3 innings, and is winless since he beat the Mets on April 17. He pitched eight innings of two-run ball in his previous start, but the Braves lost 4-0 to Philadelphia.
"I think he's pitching terrific," manager Fredi Gonzalez said. "Every game he's pitched I think he's learned something."
Atlanta put at least one runner on in five of Dempster's innings, but struggled to score for the second straight 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 scampered home on Tyler Pastornicky's sacrifice fly to right.
It was the second run in 15 innings for Atlanta, which lost 5-1 in the series opener on Monday night.
The Cubs responded in the sixth. Tony Campana led off with a single to left for Chicago's second hit of the game. He moved up on Bryan LaHair's bouncer to second and scored on Alfonso Soriano's two-out double.
Soriano was the last batter for the 22-year-old Delgado, who struck out five and walked three.
"I work in my bullpen and try to do the same in the game," he said, "and I think it's working right now."
The Cubs put runners on first and third in the eighth, but shortstop Jack Wilson made a nice turn on LaHair's double-play grounder to second to end the threat.
"How about that play Wilson made?" Gonzalez said. "It's first and third and you're staring at Soriano in a two-run game in the eighth inning if you don't turn that double play. I don't know how many guys can do that."
NOTES: Braves 3B Chipper Jones made a nice diving stop to rob Dempster of a hit in the third inning. ... Cubs president of baseball operations Theo Epstein on struggling reliever Carlos Marmol: "I haven't seen any signs of him backing down, so as long as he gives the effort and faces his challenges head on we're going to support him and help him get where he needs to be to help us." ... Bourn extended his hitting streak to 12 games.