Peavy was scheduled to start for the South Siders, but instead of facing the American League Central opponent, he was moved to a morning Minor League game on the back fields. Peavy threw 81 pitches, including his three innings of work out of the slide step, which represents an adjustment he probably would not have done during a Cactus League game.
Jimenez worked five innings for the Indians, allowing two runs on seven hits while striking out three.
"I felt good," Jimenez said. "I was able to go out there and throw all my breaking balls and fastball for a strike. In the first two or three innings, I was able to command the fastball in and away. I felt good."
The White Sox's biggest damage was inflicted in the third, when they scored their two runs thanks to four straight hits.
Josh Phegley started with a single, followed by Gordon Beckham's ground-rule double to center. Phegley scored on Jimenez's wild pitch, and Beckham came home on Dewayne Wise's single to right. Alexei Ramirez followed with another single, but after Brent Morel's sacrifice bunt moved the runners to second and third, Jimenez struck out Adam Dunn and retired Paul Konerko on a fly ball to right.
"He was pretty good," Indians manager Terry Francona said of Jimenez. "He didn't really throw his off-speed pitches for strikes, but he only gave up the two [runs], and they got four hits in a row. It wasn't like he was walking people. I thought it was, for the most part, really encouraging. I think it proves to him, hopefully, that he can live with that fastball."
Cleveland scored its first two runs in the third off of Andre Rienzo, who got the start in place of Peavy in his return from the World Baseball Classic, where he pitched for Brazil. Asdrubal Cabrera drove in both runs with a two-out double, but Rienzo had a solid outing with two strikeouts and one walk over three.
Carlos Sanchez's throwing error on Yan Gomes' ground ball to short scored the go-ahead run for the Indians in the sixth, and Cord Phelps' two-run home run in the seventh off of Deunte Heath gave the Indians breathing room.
These two teams play again March 27 in the White Sox's final Cactus League contest and then meet in Cleveland from April 12-14.
Up next for Indians: Right-hander Zach McAllister -- recently named Cleveland's fourth starter -- is scheduled to take the mound Thursday when the Tribe hosts the Royals in a 4:05 p.m. ET Cactus League contest at Goodyear Ballpark. McAllister is penciled in for five innings, and Indians rotation hopeful Trevor Bauer is slated to follow with four frames. Kansas City will send righty Jeremy Guthrie to the hill. A live webcast of the game will be available on indians.com.