The Indians won the opener and the finale of the four-game series and have won six of their last nine overall. The White Sox have won or split their past four series.
Clevinger (5-2) allowed two runs (one earned) on five hits and one walk. The 11 strikeouts bettered by one his previous single-game high, which he set against the New York Yankees on May 6.
Clevinger took the mound with a 1-0 lead thanks to a leadoff homer by Francisco Lindor but gave it back in the bottom of the first when second baseman Erik Gonzalez misplayed a leadoff grounder by Yolmer Sanchez before Jose Abreu launched a one-out, two-run homer. The White Sox would get just one more runner beyond first base against Clevinger.
The Indians tied the game in the third when Yan Gomes drew a bases-loaded walk. Lindor helped set up the go-ahead rally in the seventh when he singled against Chris Volstad (1-4) with one out, stole second and scored on Ramirez's homer.
Gomes scored an insurance run in the eighth when he came around from second on an error by pitcher Juan Minaya.
Neil Ramirez and Oliver Perez combined to allow a hit in the eighth before Cody Allen earned his 13th save by striking out the side in a one-hit ninth.
White Sox starter Carlos Rodon didn't factor into the decision after allowing two runs on two hits and three walks while striking out four over five innings. It was the second start of the season for Rodon, who missed the first two-plus months recovering from shoulder surgery.
Abreu, Kevan Smith and Charlie Tilson had two hits apiece for the White Sox.
--Field Level Media