The Braves scored three runs in the seventh and chased David Buchanan (0-4) while snapping a four-game losing streak. Chris Johnson had an RBI single and Eric Young Jr. delivered a go-ahead double that lifted Atlanta to a 3-2 lead. The Braves scored two more in the eighth.
Jason Grilli worked a scoreless ninth for his seventh save.
Shelby Miller (3-0) allowed two runs and three hits over six innings in his third straight win.
Ryan Howard hit a two-run homer for the Phillies.
Miller had his fourth steady outing of the season, always keeping the Braves in the game even without flashy numbers. He hasn't pitched more than six innings in a game and hasn't allowed more than two runs.
His lone slip came in the fourth when Howard's second homer of the season landed in the shrubs beyond the center-field fence. Howard, batting .180 entering the game, hit his third career homer off Miller.
Miller and Buchanan were locked in a breezy duel in a game that needed about an hour to play five innings. Buchanan had a six-pitch first inning and needed only 25 to get through three.
Buchanan was helped in the sixth by shortstop Freddy Galvis' diving stop-and-tumble to nip Nick Markakis at first. Galvis snared the ball that was headed to center, rolled and threw a one-hopper from his stomach for the out. He needed help off the field but stayed in the game.
Simmons got the Braves rolling with his first homer of the season. With two outs in the seventh, Buchanan walked two and Jake Diekman allowed Johnson's RBI single and Young followed with a double.
Buchanan retired his first 12 batters and was cruising before the rocky seventh. He remained winless for a Phillies team mired in last in the NL East.
Trailing 3-2, Phillies catcher Carlos Ruiz was thrown out by left fielder Johnny Gomes while trying for a double. The call stood after a brief replay review.
Braves: Atlanta's defense is suddenly hurting. The Braves made four errors on Friday night and another one on Saturday.
Phillies: Closer Jonathan Papelbon was available to pitch, though he suffered earlier in the day from a migraine. ... RHP Chad Billingsley made his third rehab start on Saturday night. Billingsley, who is trying to recover from two right elbow surgeries that limited him to 12 innings the last two seasons, allowed seven runs in five innings for Triple-A Lehigh Valley. He was expected to make at least one more start in the minors.
Braves: RHP Trevor Cahill (0-2, 9.95 ERA) has pitched only 6 1/3 innings total this season in two starts. His lone career win against the Phillies came in relief in 2013. Cahill is 3-14 the last two seasons.
Phillies: RHP Jerome Williams (1-1, 3.71 ERA) goes for his second straight win. He allowed three runs in six innings in his last start against Miami.
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