Twins starter Michael Pineda (1-0) gave up just one unearned run in five innings. The right-hander struck out five, walked two and allowed four hits.
Garver broke a 1-all tie and put the Twins ahead for good when he hit a solo shot to right field off Brewers starter Adrian Houser (0-1) with one out in the fifth.
Pineda got out of a bases-loaded jam in the bottom half of the fifth by striking out Avisail Garcia.
Minnesota broke the game open in the sixth with four runs off reliever Drew Rasmussen. Kepler hit a two-run single and Sano followed with a two-run homer.
Hiura is a converted second baseman who had never played first base before this season. He switched positions to make room for Kolten Wong, a two-time Gold Glove second baseman who signed with the Brewers in February.
One encouraging sign for the Brewers was the way Houser performed as he attempts to bounce back from a 2020 season in which he went 1-6 with a 5.30 ERA.
Houser struck out four while allowing two runs, four hits and two walks in five innings.
Twins: CF Byron Buxton left in the third inning with an illness unrelated to COVID-19, according to team officials. Buxton, who homered in each of the Twins’ first two games, doubled in his only plate appearance Sunday.
Brewers: Assistant athletic trainer Dave Yeager spent the night in the hospital after appearing to collapse in the bottom of the ninth inning of Saturday’s game while assisting home plate umpire CB Bucknor, who had been hit in the throat area with a foul ball.
Milwaukee manager Craig Counsell said Sunday that Yeager was lightheaded and “extremely dehydrated” after the game but had started feeling better. Counsell was hopeful that Yeager would get released from the hospital sometime Sunday.
Twins; Start a three-game series at Detroit on Monday. Scheduled starters are Minnesota’s Jose Urena (0-3, 5.40 ERA for Miami last year) and Detroit’s Matt Shoemaker (0-1, 4.71 for Toronto) in a matchup of right-handers.
Brewers: Open a three-game road set with the Chicago Cubs on Monday. LHP Brett Anderson (4-4, 4.21) pitches for the Brewers. The Cubs are expected to start RHP Trevor Williams (2-8, 6.18 with Pittsburgh).