The Brewers jumped on Wolf in the top of the first, scoring three runs on four hits, a walk and an error.
Back-to-back doubles by Braun and Jonathan Lucroy produced the first Milwaukee run. Lucroy then scored on a single by Carlos Gomez, who came home after a line-drive single by Rickie Weeks slid past left fielder Christian Yelich for an error. Trailing, 3-0, with one out, Wolf allowed a walk before setting down the next two Brewers to get out of the inning after throwing 26 pitches to eight Milwaukee batters.
Marlins manager Mike Redmond said Wolf's performance did not mean the veteran left-hander would be immediately sent back to the bullpen.
"I guess we weren't really sure what to expect of him," Redmond said of Wolf, who was signed and thrust into the rotation after ace Jose Fernandez had season-ending Tommy John surgery. "It was a grind; it was a struggle obviously.
"We've talked about [how] Jose's spot is going to be tough to fill. We'll see where it goes from here. We're trying to figure out what is going to be best, if it's bringing in a younger guy and let him pitch or continue to stay with Wolfie and see if he can eat up some of those innings."
Redmond said one positive about Wolf's start was that he lasted five innings, saving the bullpen extra work as the Marlins head immediately to Washington for a three-game series against the Nationals, who swept the Marlins when they most recently visited D.C.
"That was huge, because really at the beginning of that game it looked like he was going to have trouble getting through the second," Redmond said. "So that ended up being big to get as many innings out of him as we possibly could to save the other guys going into Washington. We still feel like our bullpen is in good shape."
Braun was 4-for-5 on the afternoon, including a triple and double, with an RBI, as the Brewers pounded out 14 hits against Miami pitching.
Wolf's woes continued in the second, as the Brewers tacked on two more runs. Braun reached the halfway point of a cycle -- he finished needing a home run to complete it -- when he tripled with one out to drive in Jean Segura, who reached on a fielding error by shortstop Adeiny Hechavarria.
Nelson, meanwhile, making his first start for the Brewers this season in place of the injured Yovani Gallardo, made the most of his opportunity after being called up from Triple-A Nashville. The 24-year-old right-hander scattered five hits, struck out six and walked three in 5 2/3 scoreless innings. Afterward he was sent back to the Minors.
"I thought it was all right," Nelson said of his performance. "I battled myself mechanically all day. I didn't have my best stuff, but the guys did a great job of picking me up, scoring those five runs those first couple of innings."
Milwaukee stretched its lead to 5-0 when Lucroy hit his second double, a soft line drive down the right-field line that scored Braun. Wolf faced 14 batters and needed 42 pitches to get through two innings.
"It's pretty simple when I don't pitch well; it's a matter of executing pitches," Wolf said. "Especially early on, everything was up, and a few times I painted myself in a corner with the count I was in. And when you get in those kind of situations and you don't make good pitches against a good lineup, it's hard to be successful."
Wolf handled the tough outing, his first Major League start since Sept. 22, 2012, with the poise of a veteran who has dealt with a disappointing performance.
"It's not the first time I've had a bad game," Wolf said. "The only thing that I take out of this game for the next is that things got better as the game went on. … I've never been one of those guys who can overpower guys, so I've got to be smart and throw good pitches."
The Brewers added another run in the third, when Khris Davis doubled with one out and Martin Maldonado followed with a run-scoring single to make it 6-0.
Wolf finally kept the Brew Crew off the scoreboard in the fourth, but not before Braun singled for his third hit of the game.
The Marlins squandered a scoring opportunity in the fifth when they loaded the bases with one out on back-to-back singles by Hechavarria and Jeff Mathis and a walk to Yelich. But Nelson pitched out of the jam by striking out Derek Dietrich and inducing an infield pop fly by Stanton, the Marlins' best hitter with runners in scoring position.
Milwaukee stretched its lead to 7-0 in the eighth on an RBI single by Scooter Gennett, with Miami getting on the board on Marcell Ozuna's ninth-inning home run, his ninth of the season and 31st RBI.
Redmond did not seem overly concerned that the Marlins, who have the best home record in the Majors, dropped a series at Marlins Park and now head to Washington against the Nationals, who are only a half-game behind the second-place Marlins in the NL East standings.
"I think they're all important," Redmond said of the series against the Nats. "No more important in May, whatever the date is, than it is two weeks from now or three weeks from now. I think we're playing good baseball. I think we definitely have some areas where we need to get better in, and that's a work in progress, but I love the effort, and that's all around.
"These guys come and they bring it every single day, and I'm happy with that. If we stay with our approach, we'll be fine. We have a chance to go to Washington and hopefully go in there and play our game with confidence and hopefully get a couple of wins."