Floyd (1-1) handcuffed the Tigers on three hits, issuing three walks and striking out six as the Chisox clinched their three-game weekend series at Comerica Park.
Tigers starter Adam Wilk (0-1), making his first major league start, lasted five innings, allowing two runs on three hits before leaving due to a bizarre accident.
The hurler was sitting on the bench in the top of sixth inning when teammate Prince Fielder fouled off a pitch that flew into the dugout and hit him. Wilk was seen holding his arm in pain after the blow and didn't return.
Brennan Boesch drove in the only run for the Tigers.