Floyd (2-3) dominated Boston in the outing, yielding one run on three hits while issuing only one walk.
The Chisox right-hander has allowed only two runs over 14 innings and fanned 15 batters in his last two starts.
Addison Reed tossed an inning of shutout relief and Matt Thornton earned his first save as the White Sox salvaged one win in their four-game series against the Bosox.
Adam Dunn cracked a two-run homer in the first inning for Chicago.
Josh Beckett (2-3) allowed three runs on six hits in a 6 2/3-inning start for the Red Sox.
The loss broke a six-game Boston winning streak.