"This was a really nice ballgame," Brewers manager Ron Roenicke said. "He came out with a great fastball, he located it well, it had life on it. His sliders were outstanding. He threw good curveballs, so yes, I thought this was a really good game for him."
Garza (3-4) scattered six hits over 6 1-3 scoreless innings against the team that brought him to the big leagues in 2006. Garza, signed to a four-year contract as a free agent, struck out eight and walked two for his first win since May 5.
"I've been feeling good," Garza said after his best outing since his first start of the season, when he allowed one run and two hits in eight innings of a 1-0 loss to Atlanta. "Baby steps. I've felt great. My mechanics are where I want them to be and I'm getting back to where I've been."
Kyle Gibson (4-5) allowed four runs and six hits in six innings. Gibson has won just one of his last eight starts after winning his first three.
The Brewers took a 2-0 lead in the fourth on consecutive RBI singles by Jonathan Lucroy and Carlos Gomez. Reynolds followed Scooter Gennett's leadoff double in the fifth with an opposite-field shot to right for his team-leading 13th home run to make it 4-0.
"I just made the wrong pitch," Gibson said. "I had a guy on second with less than two outs and I had gotten Reynolds away his first at-bat. And any good hitter right there is trying to move the runner over to third. And I got beat on not my best pitch. I threw him a four-seamer away and the sinker's obviously my best pitch. A sinker there, I'd probably feel a whole lot better about it. Should have gone in. He was trying to hit a ball the other way and I gave him the pitch he needed to do it."
Milwaukee added an unearned run in the seventh and another on Lucroy's third homer in the eighth.
After three perfect innings by Gibson, Jean Segura opened the fourth with his sixth bunt hit of the season. Segura advanced to second on Ryan Braun's groundout and scored on Lucroy's single up the middle, with Lucroy going to second on the throw.
Gomez followed with another single back through the box.
"They earned their way on," Gibson said. "The great bunt by Segura to start the inning, then Lucroy hit the ball up the middle. I got Gomez in a good situation, threw him a good slider and he did what good hitters do, he put the ball in play and found the hole with it."
Milwaukee scored in the seventh on consecutive two-out errors by third baseman Trevor Plouffe.
Minnesota, which stranded nine runners, squandered several scoring chances against Garza.
Joe Mauer doubled with one out in the first, but was stranded at third. Mauer doubled again to open the fourth and did not advance. In the fifth, Gibson singled with two outs for his first major league hit and Dozier followed with a double, but Mauer struck out to end the inning.
"It was more about keeping the runs off the board," Garza said. "We had some momentum and the last thing I wanted to do was go out there and break it. Mauer is a great hitter. He already hit two doubles and I just basically said, `If you're not going to hit this, no one is.'" I just tried to get it really far in there. He swung and it worked out."
Brewers 3B Aramis Ramirez, on the 15-day disabled list with a left hamstring injury, went 2 for 4 as the designated hitter in his second rehab game for Class-A Wisconsin. Ramirez is expected to be activated for Wednesday's game at Minnesota and could be the DH in the American League ballpark. ... It was the first of four consecutive interleague games between the Brewers and Twins, two in Milwaukee followed by two in Minnesota. ... Gibson's soft liner just beyond the reach of Gennett at second was his first hit in four major league at-bats. ... Mauer's two doubles gave him 290 for his career, moving him past Justin Morneau for fourth place on the Twins' all-time list (since 1961). ... Brewers reliever Will Smith has made 14 consecutive appearances without allowing an earned run, covering 13 2-3 innings.