Atlanta also had runners at first and second with two outs after Henderson walked Justin Upton and B.J. Upton in the ninth, but Uggla flew out to center to end the game.
"We had a couple of opportunities here and there," Uggla said. "We need to start taking advantage of those."
Peralta won for the second time in his last eight starts, giving up two singles to go with four strikeouts and four walks. It was the first time all season he gave up fewer than two runs in a game and was asked afterward if it was his best game of the season.
"Yeah, for sure," Peralta said. "I kept the ball down all day. . I think this was the best one so far."
Francisco Rodriguez pitched the eighth and Jim Henderson the ninth for his 10th save.
Segura finished with three hits, including his 11th homer of the season, and Aoki added three singles after the birth of his son on Thursday.
Segura's solo homer to lead off the fifth gave Milwaukee a 2-0 lead.
"I was just trying to get a base hit," Segura said. "I was just trying to put a good swing on it and I got it."
In the first, Aoki and Segura singled before Carlos Gomez was hit by a pitch to load the bases. Aramis Ramirez gave Milwaukee a 1-0 lead on a sacrifice fly. Gomez was picked off first and Juan Francisco popped out to end the rally.
NOTES: Milwaukee owns a seven-game home winning streak against the Braves. . Atlanta placed infielder Ramiro Pena on the 15-day disabled list (retroactive to June 17) due to a right shoulder strain and recalled infielder Paul Janish from Triple-A Gwinnett. . With Aoki back from the paternity list, Milwaukee optioned Josh Prince back to Triple-A Nashville. . Brewers' right-hander Donovan Hand will make his first major league start Saturday. He is 0-0 with a 3.38 ERA in nine relief appearances this year.