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"He's a monster right now," teammate Paul Konerko said of Dunn, who has put a miserable first season in Chicago last year behind him.
"I think he's an ever better hitter and better everything than he was even when he was having those great years before," Konerko said. "I think his best is ahead of him."
Dunn became the fourth fastest White Sox player to reach 30 homers -- based on games (96) -- and how has more long balls this season than he does singles (29).
"I care about hitting the ball as hard as I can. If I do that and get a single, sometimes that's OK. I'm not here to hit singles," Dunn said.
"When you get a homer, you don't really swing too hard. It just kind of shows up."
The victory allowed the White Sox to move into a tie for the division lead with Detroit, which lost at Cleveland.
Josh Willingham homered twice for the Twins, his 24th and 25th of the season.
Konerko was 4 for 4 for the White Sox with his 16th homer of the season.
"My job is to try to be as tough as I can so they don't walk him [Dunn]," Konerko said.
Dunn hit a two-run homer off lefty reliever Tyler Robertson to make it 4-all. Casey Fien (1-1) relieved and gave up a single to Konerko, a double to Alex Rios and an intentional walk to Alexei Ramirez before Viciedo followed with his go-ahead two-run single.
Dunn added a two-run double and Ramirez had a two-run homer in a five-run eighth to put the victory away.
"A really good game until about the seventh inning, and they kind of ambushed us. We didn't make any pitches. They put some in the seats," Twins manager Ron Gardenhire said.
"We didn't throw it over. We get ahead in the count and couldn't put a hitter away. .... They were swinging away, just absolutely killed us for two big innings."
Cole De Vries made his major league debut against the White Sox on May 24 when he gave up six hits and six runs -- three earned -- in five innings. He was much more effective this time, giving up an unearned run in the first and yielding a solo homer to Konerko in the fifth during his six-inning stint.
"That Konerko one was real frustrating because when I was out there I felt like I made a pitch I wanted to," De Vries said. "But he was sitting inside on that. He's a good enough hitter where if he gets a pitch he's looking for he's probably going to do something like that."
Konerko's two-out high fly just cleared the wall in left field and put Chicago ahead 2-1. Chicago got an unearned run in the first on a two-out throwing error by shortstop Brian Dozier that followed a single by Dunn and double by Konerko.
Willingham's line drive homer to center in the fourth tied the game. Quintana allowed eight hits and four runs in 6 1/3 innings.
- Umpires conferred and reversed a call in the seventh just before Dunn's homer. Chicago's Alejandro De Aza hit a sinking liner to right fielder Darin Mastroianni that was initially ruled a hit. But after an umps' conference it was changed to a catch, even though a replay appeared to show the ball hitting the ground right before Mastroianni got his glove under it.
- Willingham now has 12 career multihomer games, including two this month.
- Chicago catcher A.J. Pierzynski sat out the game with a mild strain of his right oblique, an injury he got swinging the bat Monday night. He'll also sit out Wednesday afternoon's finale.
- Justin Morneau was back in the Minnesota lineup after a paternity leave and was the DH because of a stiff neck.