The seven RBI for the game were a career best for Konerko, who has seven homers in his past 13 games.
Mark Buehrle (9-2) went seven innings, giving up three runs on seven hits and striking out three while remaining unbeaten in his last six starts.
Grady Sizemore belted two home runs for the Indians, who lost for the seventh time in their last nine games. Shin-soo Choo added a solo shot.
Choo's homer in the sixth staked Cleveland to a 3-1 advantage that held up only until the White Sox' half of the inning when the hosts tallied five runs and grabbed a 6-3 lead. Jeremy Sowers (2-7) loaded the bases before Chris Perez was brought in to pitch to Konerko, who sent a 2-0 pitch into the left-field seats.
Gordon Beckham gave Chicago their sixth run later in the inning with an RBI double.
The outburst doomed Sowers to his fourth road loss of the season and a 0-6 lifetime mark against Chicago.
The White Sox continued to roll in the seventh with four runs on two-run homers by Ramirez and Konerko off Winston Abreu.
Copyright 2009 by United Press International.