The White Sox's Paul Konerko hit two doubles, including an RBI double in the fourth inning.
The White Sox scored three runs in the fourth inning against Jimenez.
Zach Stewart, a candidate for the White Sox bullpen, allowed a run and three hits in 5 1/3 innings. He struck out one and walked one.
The White Sox's Brent Morel hit a two-run home run, his first of the spring, off Indians reliever Henricus VandenHurk.
Chicago's Alejandro De Aza hit his first home run, a two-run shot off Robinson Tejeda.