Mesoraco connected for his first career pinch-hit homer off Craig Kimbrel (0-1), who blew a save for the second time in five days. Kimbrel went to a full count on Mesoraco before the catcher homered into the first row in center.
Four pitches later, Choo hit his second homer of the game, giving him a team-leading seven. It was his second career game-ending homer.
Kimbrel fanned the first two batters in the ninth and was only one strike away from getting his 100th career save. He'd allowed only one homer this season, but gave up two in a five-pitch sequence.
Jonathan Broxton (1-1) retired three batters in the ninth for Cincinnati's fourth win in five games.
The comeback gave Dusty Baker his 1,600th victory as a manager, moving him ahead of Tommy Lasorda for 18th place on the career list.
The Braves led from the first inning until Kimbrel's last few pitches.
Brian McCann singled with the bases loaded in the first inning - the first hit of his injury-shortened season - as the Braves pulled ahead 3-0 against Homer Bailey. Kris Medlen limited Cincinnati to four hits in seven innings, including Choo's solo homer.
For the second game in a row, a Reds starter lasted a season-low five innings. Bronson Arroyo gave up four runs in a 7-4 loss in the series opener Monday night. Bailey allowed four runs on five hits and four walks in five innings, leaving for a pinch hitter in the fifth. Donald Lutz batted for Bailey and singled home a run that cut it to 4-2.
Joey Votto's double in the sixth extended his hitting streak to 10 games, the longest by a Reds player this season. Brandon Phillips' sacrifice fly in the eighth cut it to 4-3.
The series matches the NL's top two teams at striking out. The Braves lead the league with 297, the Reds are next at 268. Cincinnati's Jay Bruce, who leads the NL with 49 strikeouts, fanned with Votto on third base in the sixth inning. Todd Frazier struck out with two aboard in the eighth.
Andrelton Simmons hit a pair of homers in the series opener and moved up from eighth in Atlanta's batting order to leadoff. He opened the game with a double and scored the first run. He also made a sensational play in the fourth, diving for a grounder in the hole at shortstop and throwing out Bruce at first.
Simmons also made a barehand catch-and-throw to get Choo at first base in the eighth.
NOTES: Braves OF Jason Heyward, who had an appendectomy on April 22, took batting practice before the game. The Braves will decide by the end of the week whether he's ready to start a rehab assignment. ... Reds C Ryan Hanigan started a rehab assignment at Triple-A Louisville. He's been on the 15-day DL since April 21 with a strained left oblique. ... Jack Hannahan made his fourth start, all at third base.
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