Starter Randall Delgado has not gotten a win in his last seven starts, including five losses since opening the season 2-0.
Delgado allowed four runs on seven hits in 5 1/3 innings, including three runs that scored when Kris Medlen relieved him in the sixth and gave up a grand slam to rookie catcher Devin Mesoraco that erased a 2-1 lead.
"I had to go at him and you see what happens," Medlen said. "You feel bad for Randall because you hate to go in there and give up somebody else's runs, especially with the bases loaded, but I fell behind and had to go after him. You don't blame the park at all. I needed to jump ahead and I didn't and he made me pay for it."
The Braves open up a three-game series against Washington on Friday at Turner Field trailing the Nationals by one game in the National League East. Thursday's game wrapped up a stretch of 16 road games in their last 20, with the Braves going 9-7.
The Reds scored 14 of their 16 runs in the four-game series on 10 home runs. The teams combined to hit 16 home runs, 13 of which were solo.
"That was a heck of a series by us," Cincinnati manager Dusty Baker said. "I can't ever recall being on a team that beat the Braves four games in a four-game series. It's a very difficult thing to do to sweep a four-game series against a quality team like that, against anybody."
The Braves again played without third baseman Chipper Jones and catcher Brian McCann -- Jones due to a severely bruised left calf and McCann because of the flu -- and had first baseman Freddie Freeman on their bench Thursday because of blurred vision. The three players accounted for 80 of Atlanta's 210 RBIs coming into the game (38 percent).
"Most of our bats were in the dugout sitting with me, with Freeman, McCann and Chipper," Braves manager Fredi Gonzalez said. "It's tough to score runs, but you're going to go through this kind of spurt in a long season and you feel that the guys you're going to put in there are going to be OK."
The Braves managed just seven hits against Homer Bailey and the relievers Sam LeCure, Sean Marshall and Logan Ondrusek.
Two of those hits came in the ninth inning. Eric Hinske broke a 0-for-13 streak with a single to lead off the inning, and Tyler Pastornicky singled with one out. Juan Francisco, who had homered in the seventh inning, came to bat as the potential tying run, but hit into a 3-6-1 double play to end the game.
Thursday's pitching matchup was a rematch of May 14 in Atlanta. The Reds won that game, 3-1, as neither Delgado nor Bailey figured in the decision. Much like Tommy Hanson on Wednesday night, Delgado pitched well through the first five innings before running into trouble in the sixth. Unlike Hanson, he wasn't able to minimize the damage.
Delgado walked Brandon Phillips and Todd Frazier in the sixth to help the Reds load the bases. Medlen then fell behind Mesoraco 2-0 before Mesoraco deposited the next pitch into the left-field stands for his second home run of the season and his first career grand slam.
Bourn, who had 14 career home runs entering this series, hit a two-run homer with two outs in the fifth inning to give the Braves a 2-1 lead against Bailey. It was the third home run for Bourn in the last three games.
Francisco's solo homer in the seventh cut Cincinnati's lead to 5-3, but Braves reliever Jonny Venters gave up a solo home run to Drew Stubbs in the bottom half to restore the three-run deficit.