Giolito, 24, allowed three hits in 7 2/3 innings. The former first-round pick has recorded a win in each of his last seven starts.
"His outings have been fantastic," White Sox manager Rick Renteria told reporters. "I think he is showing that he is part of some of the best pitchers in the major leagues at this moment."
All of Giolito's strikeouts came in the first five innings. He struck out the side in the second, third and fifth innings.
Giolito has allowed five runs in his last seven starts. He's won eight consecutive decisions dating back to a victory over the Yankees on April 12.
"I'm just going out there with confidence every time and keeping it simple," Giolito said. "It's all about just executing the next pitch."
Chicago left fielder Eloy Jimenez hit a two-run home run in the second inning for the game's only runs.
Chicago moved to 30-33 with Saturday's victory. The White Sox trail the first-place Minnesota Twins by 12 games in the AL Central Division.