Delgado turned in a strong effort, throwing four perfect innings before surrendering a leadoff double to Giancarlo Stanton in the fifth. Stanton would score Miami's lone run on a two-out single from Bryan Petersen.
"He could do whatever he wanted tonight," Braves catcher Brian McCann said. "He put all three pitches wherever he wanted. His velocity was at 94 [mph]. When you have stuff like that, you can go anywhere you want to go, and that's what he did tonight."
Delgado would not give up another hit, finishing his outing after 6 1/3 innings, allowing one run on two hits. The righty walked just one batter while setting a career-high with seven strikeouts.
"You've got to give credit to people that deserve credit," Marlins manager Ozzie Guillen said. "Delgado, with all respect to all the people we've faced in the past, this kid was the best one we've seen so far. He's not the best pitcher we've seen, but today, he had the best stuff I've seen. We've faced some good ones. We've faced some quality pitchers. I think today this kid was at the top of his game."
The Braves put together a two-run rally in the fourth against Marlins starter Josh Johnson. McCann, who went 3-for-4, opened the inning with a double to right and later scored on a Freddie Freeman single to right.
"I got a couple of pitches up in the zone to hit," McCann said. "I worked the count a little bit, and when I got my pitch, I didn't miss it like I've been doing basically all season long. It was good to barrel some balls the other way and pull the ball down the line in the same game."
Shortly after driving in McCann to pick up his 36th RBI on the year, Freeman would leave the game with a contusion on his left index finger. The injury came when Jose Reyes tried to turn a double play but hit Freeman's hand with the throw. Interference was ruled and Dan Uggla was forced to stay at third base.
The Marlins then elected to intentionally walk Andrelton Simmons to bring up Delgado with two outs against Johnson. But the rookie drove in what would be the winning run with a single to left that capped the fourth-inning rally.
"I thought it was going to come back and bite us there with first and third and the pitcher in the eight hole," Braves manager Fredi Gonzalez said. "But we started the runners and we got lucky that he put one in the hole, and that was the difference in the game."
Johnson had a solid outing against the Braves, holding them to a pair of runs on six hits over 7 2/3 innings. But the Marlins could not figure out Delgado, and the Braves' bullpen finished off the win to clinch a series victory.
Jonny Venters, Eric O'Flaherty and Craig Kimbrel combined on 2 2/3 innings of perfect relief, with Kimbrel earning his 17th save.
"Delgado gave us a [heck] of an outing, and then we retired the last eight outs," Gonzalez said. "It was a good effort by the pitching staff today."