Konerko followed with his double that brought home Dewayne Wise with the winning run.
The comeback victory lifted the White Sox 2 1/2 games in front of Detroit at the top of the American League Central.
Chicago hit three home runs while building a 7-2 lead heading into the ninth. Adam Dunn had a solo shot in the first and a two-run blast in the third to reach 38 for the season. Alexi Ramirez hit a two-run homer in the fourth.
Both Dustin Ackley and John Jaso drove in two runs during Seattle's six-run ninth.
Despite giving up three runs in the top of the ninth, Addison Reed (3-1) was credited with the victory.
Seattle closer Tom Wilhelmsen (4-3) suffered the loss.