"We've been trying to get our closer in and we almost did," said Gardenhire, who watched Milwaukee score six runs in the final two innings.
"It was a great offensive night, we beat the ball around. We had some good performances."
Mauer went 4-for-5 with a home run and Cuddyer had two hits and walked twice.
"Pee-yew," Yost said. "We just got our tails whipped."
The Twins scored six runs in the first inning as Brewers starter Ben Hendrickson (0-2) failed to retire any of the six batters he faced. Mauer, Torii Hunter and Cuddyer had run-scoring singles, Justin Morneau added a two-run double, and Juan Castro drove in Morneau with a sacrifice fly.
"That was nice," Minnesota pitcher Scott Baker said. "That makes me a lot more comfortable."
Milwaukee scored in the bottom of the first inning when Geoff Jenkins hit a two-run homer. Jenkins' seventh drive of the season barely cleared the right-field wall.
Cuddyer also had a three-run triple in the Twins' five-run fourth inning. Morneau had an RBI single and Castro's run-scoring triple drove in Morneau to make it 11-2.
While Hendrickson didn't get an out, Baker (2-4) struck out a career-high eight in five innings. He allowed four runs and six hits with one walk to get his first win since April 14, a span of six starts.
"I felt better than the numbers show," Baker said. "It comes down to making pitches when you have to."
The six runs surrendered by Hendrickson marked the second game in a row he has allowed at least five runs in the first inning. The San Diego Padres scored five times in the first inning on May 11 against Hendrickson.
"First innings have been horrible for me the whole year," he said. "I just have to get that out of my head. I can't get out of the first inning."
Mauer hit his third homer in the fifth to make it 12-4.
"He's really on the ball," Gardenhire said of Mauer, who's hitting .336. "He's been swinging well. He had a great night tonight."
Hendrickson, a native of Eden Prairie, Minn., was taken out of the game before retiring a batter, marking the 14th time in Brewers history a starter failed to get an out. The last time it happened was Aug. 28, 1995, when Jamie McAndrew started at Chicago against the White Sox.
- Hendrickson fell to 1-10 in his career.
- Six Milwaukee pitchers combined to walk 11 batters.
- RF Cuddyer has reached base safely in 20 straight games.
- Saturday's attendance was 43,422, the 10th-largest crowd ever at Miller Park.
- RHP Boof Bonser is scheduled to make his first career start for the Twins on Sunday.
- The Twins have outscored the Brewers 23-11 in the first two games of the series.
- Minnesota's 16 runs were the most Milwaukee has allowed this year.