Mark Teahen also had a pair of hits and Ramon Castro drove in a run for the White Sox, who took the opener by a 3-1 count and have won five straight games. Chicago also crept within 3 1/2 games of the first-place Twins in the AL Central. Minnesota beat Texas earlier Saturday.
Floyd (10-11) scattered five hits and a run in his outing, fanning five with two walks.
Marco Scutaro knocked in the lone run for the Red Sox, who have dropped five of their last seven.
John Lackey (12-9) took the loss after yielding four hits and three runs (one earned) over seven frames. He struck out seven in defeat.