The Brewers' top prospect was recalled from Double-A Huntsville to start for Yovani Gallardo, who is nursing a sore left ankle. Nelson allowed five hits and three walks, but Miami went 0 for 7 against him with runners in scoring position.
Ryan Braun had four hits, including a double and a triple. The Brewers' slugger, who has been nursing a sore right side, came into the game 5 for 27 on their trip.
Miami's Randy Wolf (0-1) made his first start since September 2012 and was treated harshly. The 37-year-old left-hander, who is trying to come back from the second Tommy John surgery of his career, gave up nine hits and six runs - four earned - in five innings.
Wolf was filling in for ace Jose Fernandez, sidelined earlier this month by a season-ending elbow injury.
NL Central leader Milwaukee won two of three games in the series and improved to 18-6 against the Marlins since the start of 2011.
The Brewers went 4-6 on their longest trip of the season. They're 16-11 on the road, and last year their 16th road victory didn't come until July 14.
Miami fell to 20-8 at Marlins Park, still the best home record in the majors.
With all right-handers in the lineup, the Brewers teed off from the start against the left-handed Wolf, bunching four consecutive hits in the first inning to score three times. Braun and Lucroy hit back to back doubles, and Carlos Gomez followed with an RBI single.
Notes: Before Nelson's season debut, the Brewers were the only NL team to use just five starting pitchers this season. ... The Marlins had two infield hits to increase their season total to 59, most in the majors. ... Miami will begin a three-game series Monday at Washington, with RHP Nathan Eovaldi (3-2, 3.41) scheduled to start against RHP Tanner Roark (3-2, 3.42). ... The Brewers return home to begin a three-game series Monday against Baltimore, with RHP Kyle Lohse (6-1, 2.67) scheduled to face RHP Chris Tillman (4-2, 4.21).