Justin Upton made Miami pay with a home run, three hits and three runs scored in Atlanta's 6-4 comeback victory at Marlins Park.
Julio Teheran was efficient enough over 7 1/3 innings, giving up four runs, with one earned, while improving to 7-4.
Henderson Alvarez, laboring in six innings, gave up five runs (four earned) and four walks in his second start since coming off the disabled list.
"I think what we've seen is that when we do make a mistake, they'll make us pay for it," Redmond said. "We gave them a run there on the error.
"We don't have enough offense to give away runs. We need to secure the ball and play catch and try to get 27 outs. That's the goal. We're not able to give them extra outs. That's for sure."
Rob Brantly connected on his first home run of the season, a three-run shot in the second inning. He went 2-for-4, while Logan Morrison added two hits and an RBI, but he was picked off second base in the second, which was costly.
Adeiny Hechavarria had two hits, extending his hitting streak to nine straight games.
But the bottom line for the youthful Marlins is they were sloppy and had their losing streak reach five games.
After going 19-11 from May 31-July 4, which was the best record in the Majors during that span, the Marlins slipped to 3-6 in July.
"We went and we competed against San Francisco and Atlanta and St. Louis when they were here," Brantly said. "We played great games and we won those games. We know what we're capable of doing. It's a matter of building that consistency every day.
"That's going to be the difference maker, when we started doing that as a team -- staying locked in, everybody for the whole game. That's when the turnaround is going to happen."
Carrying over momentum from Monday's 7-1 win in 14 innings, the Braves put the pressure on the Marlins all night. In six of nine innings they led off with hits, and scored in five of those frames.
"You know, I always talk about those shutdown innings, and how important they are after you score to shut down the opposing team," Redmond said. "Henderson just wasn't able to do that tonight. They jumped on him early in the count and ended up getting some big hits against him. They scored more runs than we did."
For the second time in five days, Alvarez went against Teheran.
Familiarity didn't really benefit either one, because both of them had their struggles. However, Alvarez had the rougher night of the two.
The Braves jumped out on top in the second inning on B.J. Upton's sacrifice fly to right, which scored Freddie Freeman, who led off with a double.
"He came out in that first inning and he was lights-out," Brantly said of Alvarez. "He was competing and getting ahead in counts, making all his pitches, quality pitches. After that, I think we started nitpicking the zone too much. We started getting in hitters' counts. As long as we keep them on the defensive, I think we'll be all right."
Miami capitalized on third baseman Chris Johnson's error in the second inning and scored three unearned runs. All came home on Brantly's shot to right field, the catcher's first homer of the season coming on his 175th at-bat.
The lead was short-lived, as the Braves pulled even in the third on Justin Upton's RBI double and Brian McCann's sacrifice fly.
In the third inning, the Marlins claimed a 4-3 lead on Morrison's RBI single to right.
From there, the Marlins floundered, and the Braves rallied with runs in the fifth, sixth and seventh innings to grab a two-run edge.
In the fifth inning, Justin Upton doubled and scored on McCann's single. And in the sixth, B.J. Upton, who singled, scored from second on Teheran's swinging-bunt infield single, coupled with Alvarez's throwing error to first.
Justin Upton added insurance with a home run off Ryan Webb to open the seventh.
The Marlins claimed two of three at Atlanta a week ago, but the Braves secured the series win and seek a sweep on Wednesday afternoon.
Since the opening of Marlins Park last year, the Braves have won 12 of 14 meetings in Miami.
Teheran was able to provide the Braves with a quality start the night after the bullpen was stretched thin.
"We needed that type of outing after going 14 innings and having two or three guys in the bullpen who were unable to pitch, or we didn't want them to pitch," Braves manager Fredi Gonzalez said. "He did a great job. He had that good sinker. He had some changeups, and he threw some sliders."