Carlos Quentin hit a three-run homer in the fifth inning, Gavin Floyd shut down the Indians on four hits into the eighth inning, and the Chicago White Sox took the opener of a three-game series at Progressive Field, 3-0.
Cleveland starter and loser Carlos Carrasco (8-8, 4.25 ERA) worked out of trouble early, but could not escape the fifth, when Quentin went deep with two aboard and one out.
The Indians threatened to get right back in it when they put two aboard in the bottom of the fifth, but Jason Kipnis, in only his second career at-bat, flied out to end the threat.
The Tribe also put two on with one out in the eighth, but pinch-hitter Carlos Santana grounded out, and Chicago reliever Matt Thornton got pinch-hitter Orlando Cabrera to fly out.
Sergio Santos came on in the ninth with two outs and one on and got Matt LaPorta to strike out to end the game.
Floyd went 7.2 innings to lower his ERA to 4.11 as the White Sox improved to 5-1 against Cleveland in 2011.
The Detroit Tigers were having their way with the Minnesota Twins, so the Indians are likely to fall a game and a half behind the Tigers. The Tribe has not trailed in the AL Central by that much since early April.