Backed by early run support in the form of a four-run first inning, Turner limited Atlanta to two runs on four hits while striking out five. The 22-year-old, who opened the season at Triple-A New Orleans, rebounded from a loss at St. Louis.
In seven of his eight starts, Turner has allowed three runs or fewer.
The Marlins were banking on a strong pitching performance to win for the first time since July 4 at Atlanta.
Miami salvaged the series finale after dropping two tough decisions to the first-place Braves.
"All in all, I think it was a nice day," manager Mike Redmond said. "We stopped the losing streak and played a real clean game. It's nice to get back in the win column."
Atlanta has repeatedly frustrated Miami at Marlins Park. In the two seasons the stadium has been open, the Marlins are now 3-12 against Atlanta at home.
"They've got a lot of guys who can hit home runs," Turner said. "You want to keep as many guys off base as possible, because with one swing, it can really change the game.
"I had a few two-out walks that got my pitch count up, but other than that, I was able to make my pitches when I needed to."
After the Marlins' big opening frame against lefty Paul Maholm, they were able to hold on. It wasn't always easy as they left 12 on base and went 4-for-14 with runners in scoring position.
Giancarlo Stanton had a two-run double in the first, and Polanco added an RBI double in the same inning. Adeiny Hechavarria had two hits and matched his career-high hitting streak of 10 games, set last year while he was with Toronto from Sept. 16-29.
"We needed that," Redmond said. "We needed to jump out to a quick start, and kind of settle everyone down, especially Jacob. We were able to give ourselves a little room to breathe. We had several more chances to add on runs, which we've got to do a better job of down the road. We had a nice eighth inning there."
After squandering numerous chances to add on runs, Polanco came through with a two-out, two-run single in the eighth inning to open a four-run cushion in the ninth for Steve Cishek.
In a non-save situation, Cishek threw a scoreless inning, working around two singles.
Juan Pierre got the inning going with a pinch-hit single, and Ed Lucas singled for the second time in the game. Marcell Ozuna drew a full-count walk to load the bases for Polanco, who capped a three-hit game with his single to center.
"The Braves [relievers], I know they're pretty aggressive," the 37-year-old Polanco. "When they have a runner in scoring position, they try to throw the first pitch for a strike, right there. And they did. I put a good swing on the ball."
The Marlins were seeing Maholm for the first time since April 8, Miami's home opener. The left-hander had his way that night, giving up one hit over seven scoreless innings with seven strikeouts.
It was a different first inning for Maholm on Wednesday afternoon.
The Marlins posted four runs on four hits in the first inning. Justin Ruggiano walked to start the rally, and Ed Lucas singled to left. Stanton ripped a two-run double, and Polanco slapped a run-scoring double. Jeff Mathis capped the scoring with a single to right, as Miami batted around.
"[Polanco] gives you a pro at-bat," Redmond said. "You can put him in any situation, any scenario, and he gives you great at-bats. Really at a time when we needed a little more breathing room. We just needed a big hit. We had guys on base several times in several opportunities and we just needed a big hit. He was the guy who got it, and it was big for us."
Atlanta countered with a run in the second on back-to-back doubles by Chris Johnson and Dan Uggla to open the inning. A couple of key defensive plays helped limit the Braves to that lone run. Uggla was thrown out at third by Mathis after he tried advancing on B.J. Upton's strikeout. The breaking ball hit the dirt, and was blocked by Mathis, while Uggla attempted to advance.
Turner helped himself by picking Upton off at first for the second out.
In the sixth inning, Atlanta got another run, taking advantage of Turner's wild pitch. Freddie Freeman doubled and moved to third when Turner's pitch got away from Mathis.
Freeman scored on Johnson's ground ball out to first.
"He made his pitches when he needed to," Freeman said of Turner. "It's tough when you're facing a guy for the first time. We went in there thinking he was going to throw us a lot of cutters to us lefties. I didn't get one cutter the whole game. I got all two-seamers and changeups. You've just got to keep that in the back of your mind."