Trailing 7-6 entering the bottom of the 10th, Milwaukee drew even when automatic runner Carlos Sanatana scored on Willy Adames' single. Adames moved up to second on the play and advanced to third on a flyout.
Turang then delivered with two outs, sending a grounder down the third base line. Royce Lewis fielded it cleanly but his throw to first was late, giving the Brewers their fifth straight win.
Elvis Peguero (4-4) allowed Ryan Jeffers' RBI single in the top of the 10th, but he still came away with the win.
Jhoan Duran (2-6) took the loss after allowing two unearned runs on two hits in 1 2/3 innings.
Kyle Farmer gave Minnesota a 6-3 lead with his solo home run in the sixth, but Adames answered with a two-run blast in the home half of the inning. Tyrone Taylor then cranked a solo shot in the seventh to level the game.
William Contreras also went deep for the Brewers, who racked up 11 hits.
Lewis and Michael A. Taylor each hit a two-run homer for the Twins, who have lost three of their last four games.
After Carlos Correa's sacrifice fly gave the Twins a 1-0 lead in the top of the first, Milwaukee loaded the bases with two outs in the bottom of the inning. Andruw Monasterio plated a pair of runs with a single to left, but he was thrown out at second trying to stretch his single into a double.
Minnesota moved back in front with a two-out rally in the third. Brewers starter Corbin Burnes retired the first two batters on just four pitches, but Correa kept the inning alive with a single before Lewis sent a ball over the left-center field wall to make it 3-2.
Contreras opened the home half of the third with a solo shot, but Taylor responded with a two-run blast in the fourth, making it 5-3.
Burnes surrendered six runs on eight hits in six innings. Minnesota starter Kenta Maeda lasted five innings, allowing three runs on four hits.
—Field Level Media