Matt Thornton has 26 holds, leaving him four shy of tying Barry Jones' single-season franchise record of 30, set in 1990.
The White Sox rank second in the Majors with 202 homers, trailing only the Yankees, who began Tuesday with 229. The White Sox are 71-39 when hitting a homer and 43-14 with multiple homers.
Alejandro De Aza grounded into his first double play of the season in the eighth inning of Tuesday's 4-3 loss to the Indians. It came in his 571st plate appearance.
Nate Jones has thrown 21 2/3 consecutive scoreless innings over his last 19 appearances, the longest active streak in the Majors.
The White Sox have a 35-34 second-half record and saw their six-game winning streak against the Indians come to an end.