Hector Noesi struck out five but allowed three runs over 5 1/3 innings Monday against the Indians.
Tyler Flowers had a single and a solo homer in Monday's loss to the Indians.
Carlos Rodon will begin the season in Triple-A Charlotte's rotation.
Jake Petricka will open the season on the disabled list.
White Sox reassigned RHP Chris Beck to minor league camp.
Micah Johnson continued his impressive Cactus League season, going 2-for-4 with a double and a run scored as the White Sox topped the Indians 4-1 on Sunday.
Scott Carroll pitched well in Sunday's victory over the Indians, allowing just one unearned run on two hits over three innings.
David Robertson (forearm) felt good after his scoreless inning of work in Sunday's Cactus League contest.
Jake Petricka is still feeling soreness in his right forearm.
Jose Abreu went 2-for-5 with a run scored as the White Sox fell to the Athletics 10-4 on Saturday.
Jose Quintana pitched well on Saturday, limiting the Athletics to two runs (one earned) over six innings.
David Robertson (forearm) is scheduled to pitch Sunday.
White Sox reassigned LHP Zach Phillips to minor league camp.
White Sox optioned RHP Daniel Webb to Triple-A Charlotte.
Melky Cabrera clubbed his first home run as a member of the White Sox in a losing effort against the Cubs on Friday.