Broxton (2-3) entered with a 2-1 lead in the eighth and retired the first two hitters. He was then victimized by an infield dribbler that went for a single and a pair of broken-bat hits to the outfield.
"There's no way to really defense bloopers or even blame anybody for what happened," Baker said. "That was just their good fortune and our bad fortune."
Norichika Aoki hit the swinging dribbler that went for a single when Broxton couldn't field it cleanly. Aoki stole second, moved to third on a throwing error and scored the tying run when Carlos Gomez served a ball just over the glove of shortstop Wilson Valdez.
Gomez then stole second and scored the go-ahead run on a bloop double by Braun to left-center.
It was just a matter of minutes, and Broxton's day had turned ugly.
"The dribbler was just out of my reach," said Broxton, making his fourth appearance since being acquired from Kansas City in a Trade Deadline deal. "I hung a pitch to Gomez and broke his bat. Braun, I broke his bat, and nobody could get to it. They were well-placed balls."
In what has been a disappointing season to this point, the Brewers were happy to have some plays go their way.
"Hey, we finally got some breaks," manager Ron Roenicke said.
The Reds have scored only eight runs while losing four consecutive games, the team's longest losing streak since dropping four straight from June 18-22.
After the game, Joey Votto said he would accompany the team to Chicago for a four-game series with the Cubs, but he still had rehab work to do before being activated.
"I'm not ready to play yet," said Votto, who had surgery on July 17 to repair torn cartilage in his left knee.
John Axford (4-6) pitched a scoreless eighth to earn the victory. Jim Henderson pitched the ninth for his second save.
The late collapse wasted another strong performance from Mat Latos, who gave up only one run on three hits and a walk, with eight strikeouts in seven innings.
"I felt real good today," Latos said. "I was able to get into good counts, and if I did fall behind, I was able to throw a good pitch to get an out."
Latos was removed for Broxton to start the eighth after throwing 97 pitches. Broxton was brought on to pitch the eighth in front of closer Aroldis Chapman.
Baker said it was easy to second-guess the decision, but it was the correct move to bring in Broxton.
"You can look back now and say, 'Yeah, [Latos] should have gone the eighth,' but if you send him out there tired and he gives it up then it's, 'Why did you send him out there?'" Baker said. "It's not like they hit Broxton all over the ballpark."
Latos said he understood why he was removed.
"I felt all right, but we've got a good bullpen and fresh arms in the bullpen," he said. "They come in and they get the job done."
Dioner Navarro hit a two-run home run off Milwaukee starter Randy Wolf for the Reds' only runs.
Latos ran his scoreless streak to 19 2/3 innings before Gomez homered with one out in the sixth. The right-hander has a 2.03 ERA in his last nine starts.
The Reds failed to score when they had a chance to break open the game in the sixth off Wolf. Cincinnati loaded the bases with one out, but Miguel Cairo's pop fly was caught by Aoki in foul territory, and the right fielder fired home to prevent Brandon Phillips from tagging up from third.
Navarro then hit a hard shot down the left-field line, but Milwaukee's Aramis Ramirez snagged it and threw to first with Corey Hart stretching to get the one-bouncer for the final out.
"Aramis saved them with that ball down the line, that's at least two runs," Baker said. "That shows the importance of defense, and it's a game of inches."