Backed up by early run support, Nelson (1-0) pitched a career-high 5 2/3 scoreless innings, allowing just five singles with three walks and a career-high six strikeouts in his second big league start.
Nelson knew going in that his 2014 debut was intended to give righty Yovani Gallardo more time to nurse a left ankle sprain. The organization's top prospect saw it as a chance to show his progression.
"Yo's getting healthy, and it is what it is right now," said Nelson, who threw 64 of his 107 pitches for strikes. "I'm just going to keep working on my consistency down there, so hopefully next time I won't have to settle in like I did today and get ahead of hitters better."
Milwaukee jumped on former Brewer Randy Wolf (0-1) with four straight one-out hits in the first. Ryan Braun and Jonathan Lucroy put together back-to-back doubles before Carlos Gomez singled. Gomez stole second and scored on Rickie Weeks' single to left, which skipped under Christian Yelich's glove.
The Brewers extended the lead to 5-0 in the second when Braun, who finished a homer shy of the cycle, drove in Jean Segura with a one-out triple. Segura had reached on an error. Lucroy followed with his second RBI double of the game.
At that point, after 1 1/3 innings, the offense had produced more runs (five) than outs recorded and as many extra-base hits (four).
"Guys put some really good at-bats together [with] really big hits in big situations," said Lucroy, who went 3-for-5 with two run-scoring doubles.
Nelson, meanwhile, struggled to find his command. He threw first-pitch strikes to just three of the first nine Marlins batters but worked out of a jam in the second. Marcell Ozuna walked with one out and moved to third on Jeff Mathis' single. After falling behind Wolf, 3-0, Nelson came back to induce a popout to second.
The 24-year-old escaped a bases-loaded situation in the fifth to qualify for the win. After Nelson retired seven in a row, Adeiny Hechavarria led off with a bunt for a base hit, and Mathis singled to put runners at first and second. Nelson struck out pinch-hitter Jeff Baker with a 94-mph fastball but walked Yelich to load the bases. He caught Derek Dietrich looking at an 84-mph slider and got Giancarlo Stanton to pop out to second.
Marlins manager Mike Redmond described Nelson as "effectively wild."
"He had some nice life to his fastball," Redmond said. "We definitely had some opportunities to get to him and put some pressure on him, but it seemed like every time we had a big chance, he buckled down, made a couple good pitches and was able to get out of it."
Miami chased Nelson with a two-out rally in the sixth. Ozuna reached on an infield hit, and Hechavarria singled. Righty Rob Wooten came on in relief and forced Mathis into a groundout to third.
The Brewers added another run in the eighth with Scooter Gennett's pinch-hit RBI, and the Marlins avoided a shutout with Ozuna's home run off closer Francisco Rodriguez.
It was an encouraging end to a 4-6 trip as Milwaukee captured its first road series win since last month's visit to St. Louis. Miami boasts baseball's top home record (20-8).
When the Brewers kicked off the trip in Chicago, they were five games up in the National League Central. The Cardinals' victory Sunday kept them two games back.
"You lose today and it turns into a really bad road trip, so I think with the pitching we have and the signs of offense going into the right direction, it's good," Brewers manager Ron Roenicke said.