The victory gave the AL Central-leading Twins a 2-1 series win over the Brewers, who dropped to 2-6 at home.
Minnesota starter Kenta Maeda (3-0), in his first season with the Twins after being acquired from the Dodgers in February, retired the first 11 batters he faced. He allowed two runs in 6 2 / 3 innings, striking out five and walking one. He entered the game with 16 strikeouts and three walks in 17 innings.
Brewers left-hander Eric Lauer (0-2), acquired from the Padres in November, had lasted only three innings and given up six runs in his first start. On Wednesday, he surrendered seven runs in 3 2/3 innings.
"It felt like there was a lot more just kind of bad baseball luck happening there," Lauer said. "I was making some competitive pitches, wasn't getting a whole lot of calls, just wasn't attacking as much as I should have been."
The Twins set the tone in the second inning, jumping to a 5-0 lead on a ball that was hit into the sun, four consecutive singles and a wild pitch.
Jake Cave drove in the first run with a line-drive double that froze left fielder Christian Yelich for several seconds as he used his glove to shield his eyes from the sun. Mitch Garver scored on Nelson Cruz's broken-bat single into center field.
"Those are the kinds of innings that you want to stay in the dugout, you want to keep hitting," Garver said.
The Twins led 12-0 before Milwaukee pushed across its two runs in the sixth inning on a single by Luis Urias.
The 12 runs is the most given up by Brewers pitchers this season. Of the Twins' nine starting batters, only Garver did not have an RBI.
"You look at the lineup from top to bottom, it was an explosive night and unrelenting, and that's what we're looking for," said Twins manager Rocco Baldelli.
Milwaukee third baseman Jedd Gyorko made his third career appearance on the mound, pitching a scoreless ninth inning.
Twins: Baldelli expects right-hander Zack Littell (left hamstring strain) to be activated by the time the team returns home Friday.
Brewers: With one out in the fifth inning and a 2-1 count on Marwin Gonzalez, right-hander Justin Grimm was removed. He had a callous on his index finger "that basically came open," manager Craig Counsell said.
Entering Wednesday, Twins right-hander Randy Dobnak (3-1) led the majors with an ERA of 0.90.
In four outings, Brewers left-hander Josh Hader has three saves and has yet to allow a run or a hit. Opposing batters are 0-for-12.
Twins: Thursday is their second off-day this season. On Friday, they host the Royals in the first of 20 straight games.
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