Floyd (6-7), who came into the contest with an eight-start losing streak against the Twins, stranded a pair of runners at third in the early going and then settled down to stifle Minnesota on five hits.
The right-hander didn't issue a walk and struck out nine for the first-place White Sox, who increased their American League Central lead over Cleveland to 1 1/2 games.
The Indians fell 6-4 to the New York Yankees Tuesday.
Addison Reed earned his 10th save in the ninth inning, but not before the Twins scored twice on Jamey Carroll's single. The Chicago closer finally induced Denard Span to ground out with a runner in scoring position to end the game.
Liam Hendriks (0-5) yielded three runs on five hits in a 6 1/3-inning start for Minnesota.