Over his past seven starts, Rodon has turned in a 1.66 ERA and .193 opponents' average over 48 2/3 innings for the White Sox.
The Indians made things interesting in the ninth inning, when Chris Johnson launched a two-run homer off White Sox closer David Robertson, but that is as far as Cleveland's rally went, as Abraham Almonte, who singled with one out, was picked off to end the game.
Right-hander Carlos Carrasco took the loss after giving up three runs (two earned) on four hits in five-plus innings for the Indians (73-74), who dropped four games back of the Astros in the race for the American League's second Wild Card spot.