"Everybody was great except for me today," said Phil Hughes, who lasted just five innings but got the win.
He allowed eight hits and tied a season high by giving up five earned runs. Hughes (8-3), who went at least six innings in his 11 previous outings, allowed his first walk in 107 batters during the White Sox's five-run third inning.
"I just struggled with command, my off-speed stuff wasn't great," Hughes said. "Our bullpen stepped up big today, offense fought back a couple times. That's huge."
"Anytime you sit there and pity yourself, youre going to get buried. Nobody cares. You have to be able to pick yourself up off the mat and compete and then it works out," said manager Robin Ventura.
The Twins last swept Chicago in a four-game series June 9-12, 1994.
"Anytime you sweep anybody is a real good feeling, but anytime you get a four-game it makes it that much more gratifying for our ballclub," said bench coach Terry Steinbach, who took over when manager Ron Gardenhire was ejected in the third inning after arguing with home plate umpire D.J. Reyburn.
On an overcast, humid afternoon, Hughes wasn't the only starter who struggled.
In his past five starts for Chicago, John Danks (6-6) was 3-1 with a 1.51 ERA, allowing just 24 hits.
However, none of those were against Minnesota, a team he has struggled against. Danks allowed six earned runs on a season high-tying 10 hits. In his last eight starts versus the Twins since Aug, 11, 2010, he is 0-6 with a 6.18 ERA.
"It's just one of those days, I guess. Certainly wasn't fun. Shot myself in the foot. Didn't do myself any favors. Cost us the game," he said. "You score five runs, that should be plenty to win a ballgame. To go out and give it right back in a five-inning span is kind of a tough pill to swallow."
The left-hander walked the first two batters he faced, but the Twins managed just one run. Minnesota, however, scored twice in the second for a 3-0 lead.
Kurt Suzuki led off with a double, but was thrown out at home trying to score on a single by Eduardo Escobar. Escobar scored one batter later on Sam Fuld's double off the right field wall. Mauer added an RBI single later in the inning.
Mauer has six RBI in his last four games, after entering the series with just 16.
"When Joe Mauer heats up, you watch out around the league," Dozier said.
Hughes gave up the lead in the third.
A pair of singles and a walk loaded the bases with no outs. After Adam Eaton struck out on a full-count pitch, Beckham lined the first pitch he saw for a two-run double to the wall in left-center and Abreu followed with a two-run single up the middle for a 4-3 lead. A bloop single by Conor Gillaspie plated the inning's final run.