Carlos Gomez had three hits and two RBIs for Milwaukee, while Lucroy also drove in a pair of runs. Rickie Weeks homered among his three hits for the Brewers, who tied a season high with 16 hits despite playing without Braun after he aggravated his sore right thumb Sunday against Philadelphia.
"Anytime you have one of your big boys out and you can score and do what we did and get that many hits, it's big," Brewers manager Ron Roenicke said.
Gallardo (5-6) won for the second time since April 29 and became the third Brewers pitcher to strike out 1,000 batters, joining Ben Sheets and Teddy Higuera.
"Getting 1,000 strikeouts, it's a big number," Gallardo said. "It's definitely a lot of work. It's a lot of pitches thrown. It's one of the goals and hopefully keep moving forward to get to the next one."
The right-hander allowed four hits and one walk while striking out four on 108 pitches before turning it over to Donovan Hand in the ninth.
"Anytime you go eight innings it's definitely a good day," Gallardo said.
The Marlins scored on a groundout to avoid the shutout, but have managed no more than one run in 21 of their 63 games. Miami's record is a major league-worst 18-45.
"We didn't do anything with (Gallardo)," manager Mike Redmond said. "Give him credit. He pitched well."
Marlins slugger Giancarlo Stanton went 1 for 4 in his first game since April 29 after missing 36 due to a right hamstring injury.
"It was miserable not being able to play so I was happy I was out there," Stanton said.
Ricky Nolasco (3-7) allowed a season-high 10 hits and four runs in 5 1/3 innings. Nolasco is 2-3 with a 7.58 ERA in eight starts against Milwaukee.
"All night was tough," Nolasco said. "It's one of those games you want to go as deep as you can and not kill the pen."
The Brewers got to Nolasco early, scoring two runs in the first inning on RBI singles by Gomez and Lucroy. Gomez added another RBI single in the second for a 3-0 lead.
"It's easier when you get runs early in the game, especially in the first inning," Gomez said. "Everybody has a good feeling the rest of the game to continue the good job."
Weeks' fifth home run, a solo shot in the third, stretched it to 4-0. Weeks is 9 for 20 in his last seven games to raise his batting average over .200 for the first time since April 16.
"That's a huge pickup for what we need there and hopefully this continues," Roenicke said.
Gomez tripled leading off the seventh and scored on a single by Lucroy. Juan Francisco added a sacrifice fly to make it 6-0.
Braun did not take part in batting practice and could miss the series. "It's possible," he said. ... Brewers RF Norichika Aoki extended his hitting streak to 11 games with a double leading off the game. He is batting .341 (15 for 44) during the streak. ... Marlins 3B Placido Polanco left in the sixth with lower back stiffness and is day to day. ... Miami RHP Jacob Turner (1-0, 0.69 ERA) will face Milwaukee RHP Wily Peralta (4-7, 6.16) on Tuesday.