Humber struck out five and walked two. The Giants scored their run against Humber in the first inning after a walk and a throwing error by White Sox shortstop Eduardo Escobar.
Brandon Crawford hit a single off Humber in the second inning.
San Francisco reliever Scott Munter left with a left calf strain after pitching to one batter in the third inning. He was injured while running to cover first base on a grounder by Escobar.