Floyd (3-3) struck out five before giving way to Matt Thornton with the bases loaded and two out in the eighth.
Thornton struck out Eric Hosmer on four pitches to end the threat and Hector Santiago worked a perfect ninth to complete the shutout.
The White Sox have captured three in a row. Kansas City had won back-to-back games.
Adam Dunn opened the scoring with a solo homer in the first, his 11th home run of the year and his second in as many nights.
Felipe Paulino (1-1), making only his second start of the year, allowed four runs on seven hits over 5 2/3 to take the loss.