The win was Chicago's second straight following a five-game skid and their 10th in their last 12 games at U.S. Cellular Field, which sold out for the second consecutive night.
The 34,715 in attendance marked the third sellout of the season for the White Sox.
"Like I said last night, when big situations come up and 35,000 people get into the game, you get a little extra adrenaline hitting," White Sox designated hitter Adam Dunn said, "and it seems like the pitcher wants to make the perfect pitch and sometimes they overdo it and leave something up."
After being held to two runs -- one of which was unearned -- by Twins starter Cole De Vries, the White Sox put up a four-spot in the seventh. Dunn hit his Major League-leading 30th home run, a two-run shot, off left-hander Tyler Robertson to tie the game at 4.
Dunn became the fourth fastest White Sox player to reach 30 home runs in a season based on a number of team games, reaching the mark in the club's 97th. Frank Thomas holds the record by hitting his 30th homer in the club's 81st game in 1994. Dunn also became only the fourth left-handed hitter in club history to hit 30 homers in a single season, joining Jim Thome (2006-08), current manager Robin Ventura (1996) and Oscar Gamble (1977).
"He's a monster right now," said White Sox first baseman Paul Konerko, who could be described similarly.
Konerko, who went 4-for-4 with a solo homer in the fifth, followed Dunn's blast with a single and Alex Rios doubled before right-hander Casey Fien (1-1) walked Alexei Ramirez to load the bases. Viciedo then singled over the shortstop's head to score Eduardo Escobar -- who pinch-ran for Konerko -- and Rios.
Konerko finished a triple shy of the cycle and homered for the second straight game after experiencing an 18-game homerless drought. The first baseman is hitting .536 with two home runs and six RBIs in his last eight games.
"We're not going to go anywhere without Paul doing what what he does," Dunn said. "People think Paul is struggling, everybody's all over him for reasons I don't know why, but he's still hitting .330."
Dunn also finished a triple shy of the cycle after a two-run double in the eighth made it 8-4. Following an RBI single by Rios, Ramirez finished off the five-run inning with a two-run homer, his third.
While Minnesota's bullpen faltered, White Sox right-hander Nate Jones (4-0) earned the win as one of three Chicago relievers to combine for 2 2/3 perfect innings.
"A really good game until about the seventh inning. They kind of ambushed us," Twins manager Ron Gardenhire said. "We didn't make any pitches, they put some in the seats, we didn't throw it over, we get ahead in the count, we couldn't put a hitter away, they did a [nice] job. They were swinging away and just absolutely killed us for two big innings."
Minnesota's Josh Willingham got the best of White Sox left-hander Jose Quintana, going deep twice and driving in all of Minnesota's runs with a solo shot in the fourth and a three-run homer in the sixth.
Willingham's fourth-inning blast broke a 12-inning scoreless streak for Quintana, who didn't factor in the decision but remains unbeaten in his last eight starts. He has a 2.78 ERA in that span.
"Willingham got him twice. But other than that, he's in every game," Ventura said. "That's one of the things he does. He finds a way to work through a lineup and Willingham got him, but we wish we could have got him a win."
Quintana's counterpart, De Vries, scattered seven hits in six innings. Aside from Konerko's homer, the only other run he allowed came in the first, when Dunn scored on an error by Twins shortstop Brian Dozier, whose throw to first on a two-out grounder by Rios pulled Joe Mauer off the bag.