Giolito, 24, walked only one Houston hitter in winning his first major league shutout. Giolito (6-1) has won four consecutive starts.
"This was my first real [complete game]," Giolito told reporters.
White Sox manager Rick Renteria said he wasn't concerned about letting Giolito go the distance. Giolito threw 82 of his season-high 107 pitches for strikes Thursday night.
"You don't want to disrupt how they're feeling," Renteria said. "As a manager, if you're going to talk to them in the eighth, you might as well just take them out. Just let them keep flowing and concentrating on what they're doing. And he did it. He did a great job."
Giolito has a 2.77 ERA in nine starts this year. He had a 6.13 ERA and allowed 27 home runs in 32 starts last year.
The young right-hander has only given up three home runs in 52 innings this season.
"He generated a ton of swing and misses, soft contact. We got four hits," Astros manager AJ Hinch said. He came in and really commanded the game from the very beginning."
Thursday marked the first nine-inning complete game by a White Sox pitcher since Chris Sale in Sept. 2016. Sale threw the team's last shutout, a two-hitter in a 1-0 victory over the Tampa Bay Rays on April 15, 2016.
White Sox rookie Eloy Jiménez hit his sixth home run of the year Thursday night.
Chicago moved to 23-26 with the win. The White Sox are only 3 1/2 games out of the second AL Wild Card spot.