The simplest of plays turned into a crucial error when usually sure-handed third baseman Juan Uribe dropped a foul pop-up in the sixth inning Thursday, a mistake so costly that even a subsequent two-run error by the opposing pitcher couldn’t offset it.

The Red Sox scored three unearned runs in the sixth inning to open a 4-0 lead on the way to a 5-2 win Thursday against the Braves on a hot, steamy night at Turner Field.

The winless streak for Braves ace Shelby Miller (5-3) is at six starts after he was charged with seven hits and four runs (one earned) in 5 2/3 innings. Boston’s only two wins in their past 10 games came this week against the Braves.

“Those things happen,” Miller said of Uribe’s error. “Obviously just bad luck. It’s not something that you can get down on, or say if it didn’t happen those (three) runs don’t score. That’s just not the game of baseball. Those things happen. I didn’t do a good job personally getting out of it. I gave up some hits over the middle of the plate that were pretty crucial at times, and they ended up putting together a big inning. I felt like that’s the reason why we lost the ballgame.

“I go out there and give up three runs again, just like last time. Not a good job.”

In his previous start Saturday at New York, Miller was pitching another gem and had a 1-0 lead until the seventh inning, when he was charged with three runs after giving up three consecutive one-out hits. The Braves came back to win that game 5-3 in 11 innings.

“Those past two games I’ve just given up big innings and we kind of dug ourselves into a hole,” Miller said. “Last time we came back and won, which was great. But that’s not always going to happen. At the end of the day, I’m just still pretty upset about it. It’s my fault we lost, simple.”

The Braves have gone 10-14 while failing to win any of their past eight series. They lost all four of their three-game series in that span, split a pair of four-gamers, and split both two-game, home-and-home series this week against the Red Sox.

Red Sox starter Clay Buchholz (4-6) let in two unearned runs in the sixth when he tried to scoop-and-shovel A.J. Pierzynski’s bases-loaded, two-out grounder, instead tossing it over the head of first baseman David Ortiz. That cut the lead to 4-2 before Andrelton Simmons flied out deep to the right-field corner to end the inning.

The Braves also put two runners on in the seventh before Cameron Maybin, the major league leader in average with runners in scoring position before Thursday, grounded out.

Braves right fielder Nick Markakis played his 393rd consecutive game without an error to set a major league record, breaking the mark by Darren Lewis during 1990-1994. But another streak ended when Braves first baseman Freddie Freeman sat out the game with a sprained wrist, ending his streak of 234 games played — 42 games longer than the majors’ second-longest active streak before Thursday.

After a 45-minute rain delay prior to the first pitch, Miller retired the first nine Red Sox batters, including five groundouts and three strikeouts. He got through the first three innings in an efficient 38 pitches, before Brock Holt tripled on an 0-2 fastball to start the fourth.

Center fielder Maybin made a leaping attempt and crashed into the wall on the play, but wasn’t close to catching it. One out later, Ortiz hit a high-chop groundout to second base that scored Holt to give the Red Sox a 1-0 lead.

Miller gave up three consecutive singles to start the sixth, the second hit by Mookie Betts after Uribe dropped his pop foul. Hanley Ramirez hit a bases-loaded double-play grounder that brought in the second run of the game, and Xander Bogaerts singled on the next pitch for a 3-0 lead

Alejandro De Aza followed with an RBI double, ending Miller’s night after 105 pitches. Ten of those pitches were required to strike out Buchholz with two out in the fifth inning, after the Red Sox pitcher took two close pitches the Braves thought were strikes, then fouled off four consecutive full-count pitches before whiffing. The Braves had intentionally walk Sandy Leon — .158 average before Thursday — with a runner at second in order to face Buchholz.

“I thought (Miller) was throwing really well; the ball was coming out of his hand phenomenal,” said Braves veteran Kelly Johnson, who filled in at third base in place of injured Freddie Freeman. “I think that (10-pitch) Buchholz at-bat, not getting the pitch called and all those foul balls, may have got to him a little bit, and with the weather, things like that. I’m sure he wouldn’t tell you that. It just felt different after that. Of course, that 20-foot hopper over my head, and Juan not making that catch – things like that happen, and the wheels kind of kept going for them.”

Miller is 0-2 in his past six starts despite a 2.94 ERA and five quality starts in that span.

“If you wouldn’t have told me that, I wouldn’t have known that,” Braves manager Fredi Gonzalez said, “because he has pitched that good, for me. He gets an extra day now with the off day, and then on to the next one.”

The Braves scored one or no runs while Miller was in the game in four of his past six starts, including no runs while he was in Thursday. He got an average of 4.5 support runs per nine innings during his first eight starts, when he was 5-1 with a 1.33 ERA.

Miller has a 1.59 ERA in six home starts, but just two home wins to show for it.

The only hit for either team through three innings was Jace Peterson’s first-pitch double to start the Braves’ first inning. Buchholz recorded 16 outs in the next 17 batters, including a Markakis double-play grounder after Maybin’s leadoff single in the fourth inning.