Reynaldo Lopez pitched five no-hit innings before leaving with dehydration and flu-like symptoms, and the Chicago went on to beat Texas 2-0 on Sunday.
Jose Abreu drove in both White Sox runs to reach 100 RBIs for the fifth time in six seasons. Adam Engel had two of Chicago's five hits.
Lopez (8-11) struck out six and allowed four baserunners while throwing 52 of 80 pitches for strikes.
Bummer, Evan Marshall, Jace Fry and Alex Colome followed with a scoreless inning each. Colome worked around a walk in the ninth to earn his 25th save.
Lucas Giolito (14-6, 3.20) takes the mound on Tuesday against Twins RHP Michael Pineda (9-5, 4.26) in the opener three game series in Chicago. Giolito shut out the Twins on three hits and struck out 12 at Minneapolis last Wednesday. Pineda is 3-0 in his last four starts.