Gavin Floyd (5-3) allowed just one run on five hits in seven innings for the White Sox, who have won three straight and improved to 9-3 in their last 12 tries.
"At that point, you get a couple runs, you want to bear down and have better focus and make sure you keep the lead," Floyd said.
Matt LaPorta had a solo home run for the short-handed Indians, who a have lost four of the last seven games.
Cleveland was without designated hitter Travis Hafner, out for a second straight game with soreness in his right ribs, and outfield Travis Buck, who was a late scratch with a left big toe injury. Alongside those injuries, the club was missing Orlando Cabrera because he was becoming a U.S. citizen in South Carolina, and center fielder Grady Sizemore is still on the 15-day DL.
Indians starter Fausto Carmona (3-4) was roughed up for eight runs in five innings. The right-hander gave up seven hits with two walks and three strikeouts.
"There are certain teams where he can get away with having not very good separation of his pitches," Indians manager Manny Acta said of Carmona. "But this is not one of those teams."
Cleveland scored first during its opening at-bat when Asdrubal Cabrera trotted home on Carlos Santana's sacrifice fly to right field. But that was all the runs the club would see until LaPorta's solo shot when the game was already out of hand in the ninth.
The White Sox answered right back in the home half of the first on Konerko's two-run double that drilled the base of the left-field wall to take an early lead.
Chicago added onto that lead with a four-spot in the second inning.
Alex Rios and Dallas McPherson started it off with singles and the bases were loaded on Omar Vizquel's bunt. Two batters later, Ramirez doubled in McPherson and Vizquel. The next batter, Dunn, finished off the rally with a two-run single.
Quentin made it a 8-1 game for the White sox in the fifth with a two-run blast.
Hafner may have a MRI on Friday when the team returns home from a weekend interleague matchup with Cincinnati...The Indians recalled infielder Luis Valbuena from Triple-A Columbus before the game and designated pitcher Justin Germano for assignment.