Peralta (5-8) 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.
Afterward, he was asked if it was his best game of the year.
"Yeah, for sure," Peralta said. "I kept the ball down all day."
Rodriguez picked up the previous five saves for Milwaukee to reach 299 in his career. Henderson was on the disabled list and then appeared in five games before returning to the closer's role against the Braves.
Segura finished with three hits, including his 11th homer, and Norichika Aoki added three singles after the birth of his son Thursday.
"I was at the hospital all day yesterday," Aoki said. "I didn't get much sleep last night."
Atlanta was shut out for the 10th time and lost for the fourth time in five games.
"It's just part of the game," B.J. Upton said. "You play long enough you are going to get in stretches like this. Just got to find a way. We are a good enough ballclub. We'll be fine."
Julio Teheran (5-4) gave up two runs and eight hits in 6 1/3 innings. He struck out five and did not walk a batter.
Segura's homer leading 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.
The Braves struggled to score for the second night in a row.
After stranding 11 runners in a 4-3 loss to the New York Mets on Thursday, Atlanta was at it again partly because of Teheran's inability to execute sacrifice bunts.
In the fifth, Atlanta got its first hit when Upton led off with a single. He went to second when Uggla flied out to deep center and advanced to third on an infield single by Johnson.
This time, Teheran attempted a safety squeeze and bunted the ball to the right side of the plate. Peralta was able to field the ball in his glove and quickly tossed it to catcher Martin Maldonado, who tagged out the sliding Upton.
"That was a nice play," Milwaukee manager Ron Roenicke said. "You've got a fast runner on third base. That play is really hard to defense. And the bunt wasn't that bad. He got over there in a hurry and made a nice flip over. Maldy did a great job of blocking the plate."
Simmons followed with a drive to right-center that was caught by a diving Aoki.
"We almost had it," Atlanta manager Fredi Gonzalez said. "We had the right guy on third base that could read it but (the bunt) could not get quite far enough down the first base line."
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 flied out to end the game.
"A couple of times tonight we could have used that one hit," Uggla said. "We had a couple of opportunities here and there. We need to start taking advantage of those."
Milwaukee owns a seven-game home winning streak against the Braves. ... The Brewers improved to 3-28 when scoring three or fewer runs. ... 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 RHP 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.
Copyright by STATS LLC and The Associated Press
MILWAUKEE, WI - JUNE 21: Julio Teheran #49 of the Atlanta Braves pitches in the bottom of the first inning against...