Luke Hochevar (7-10) coasted to his second complete game and the first shutout of his three-year major league career.
Olivo drew a bases-loaded walk in the third, hit his first two-run homer in the fourth, delivered a sacrifice fly in the seventh and homered again in the eighth. Kansas City pounded out 13 hits.
Hochevar allowed just three hits -- a lead-off single to Dewayne Wise in the third, an infield single to Scott Podsednik in the sixth and another infield single by Chris Getz in the eighth.
Mark Buehrle (12-9) was charged with the loss after giving up five runs on seven hits in six innings.
Chicago remained 6 1/2 games behind Detroit in the American League Central.
Copyright 2009 by United Press International.