Wheeler (4-4) allowed three hits, walked one and hit a batter in his first win since April 29. The right-hander went 0-3 with a 4.44 ERA in four previous May starts.
Wheeler said manager Rob Thomson asked him how he was feeling after the seventh.
"(Thomson) told me if I got the first two guys in the eighth, I would get a chance to get through it," said Wheeler, who then struck out the first two batters before retiring Matt Olson on a bouncer to first. "I worked really hard this past bullpen working up and hitting my spots."
Wheeler felt it was his best outing of the season.
"That was a very well-pitched game against us," Braves manager Brian Snitker said. "I felt like he probably could've thrown out there all day long."
"When we got those two runs, we knew that was big," Turner said. "Charlie is really good and we knew it would be tough."
Morton struck out nine in 5 1/3 innings. He allowed seven hits and walked four.
It was Kimbrel's seventh save of the season and No. 401 for his career.
Murphy had two of Atlanta's four hits. The Braves went 0 for 4 with runners in scoring position.
Turner, who has struggled in his first season in Philadelphia, had two hits and stole a base. Kody Clemens had two hits and scored a run.
The Phillies went 1 for 9 with runners in scoring position and left 12 runners on base.
Philadelphia's Alec Bohm made the game's top defensive play in the third. The third baseman made a diving stop of an Ozuna grounder with a runner on second, and threw Ozuna out from his knees. Wheeler got Rosario to pop out to end the inning.
"That was a huge play," Thomson said. "He had the presence to stay down and throw because he knew he had the time. That was a big play for us."
'SON OF PUDGE' JOINS BRAVES
The Braves recalled right-hander Dereck Rodriguez, son of Hall of Fame catcher Ivan Rodriguez, and sent left-hander Dylan Dodd to Triple-A Gwinnett. Rodriguez was claimed off waivers on May 15 and sent to Triple-A, where he made two relief appearances. Rodriguez will pitch out of the Braves' bullpen.
Phillies: LHP José Alvarado was scheduled to throw a bullpen session but threw off flat ground instead after feeling stiffness. Thomson did not feel it was a setback. Alvarado, who had five saves in 14 appearances before going on the injured list on May 8, is expected to return mid-June.
Braves: Left-handed reliever Dylan Lee has not started a throwing program since being placed on the IL on May 17 with shoulder inflammation.
The home run allowed by Kimbrel was the fifth he has given up in 20 innings this season. ... Braves CF Michael Harris II, who has battled multiple injuries this season, was hit by a pitch in the right leg below the knee in the third. He got up quickly and headed to first base. ... The Braves are 1/3 in their City Connect uniforms, which they wear for Saturday home games. ... Morton joined Clayton Kershaw (6-4 in 10 starts) as the only two pitchers with at least 10 starts this season to have a decision in every game.
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