Carmona (12-14) snapped a six-start losing streak with his most impressive showing of the year, scattering three hits and a walk while fanning seven en route to his third career shutout and first since May 12, 2008 vs. Toronto.
The 2010 All-Star hurler ended the brisk one-hour, 57-minute affair by retiring the final 16 hitters.
Matt LaPorta homered for Cleveland, which has won three of the four overall.
Carl Pavano (16-11) went a full eight innings in the loss, allowing two runs on six hits and a walk for the American League Central-leading Twins, who now hold a 5 1/2-game lead over the White Sox.