Pavano (6-4) handled the White Sox lineup with relative ease in his first shutout since May 17, 2005, for the Yankees. He faced four batters over the minimum.
After giving up a leadoff double in the first inning to Scott Podsednik, he retired the next three hitters and stranded Podsednik at third.
Pavano is 6-1 with a 3.00 ERA after going 0-3 with a 9.50 ERA in April.
Travis Hafner and Ryan Garko added back-to-back home runs in the sixth inning for the Indians.
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The White Sox have lost four in a row since a season-high four-game winning streak and have been shut out a major league-worst nine times. Chicago has not scored in 23 1-3 consecutive innings and has been blanked three of its last four games.
Garko drew a leadoff walk in the third inning and Ben Francisco walked with two outs. Then DeRosa, in his first game back in Chicago after being traded by the Cubs in the offseason, followed with a long home run to left field to give the Indians a 3-0 lead. It was DeRosa's ninth of the season.
Hafner and Garko hit consecutive home runs in the sixth inning. Hafner homered in his first game back after a stint on the disabled list with right shoulder soreness and Garko chased White Sox starter John Danks with his sixth of the season.
Danks (4-4) lasted 5 2-3 innings, allowing five runs on six hits. Danks is 1-5 with a 5.63 ERA in nine career starts against the Indians.
The White Sox played without right fielder Jermaine Dye, who served the first game of a two-game suspension for arguing with home plate umpire Mike DiMuro after being called Dye out on strikes on May 13. Dye also accidentally hit DiMuro with a batting helmet after he spiked the helmet on the ground. Dye began his suspension after his appeal was denied on Friday.