Giolito gave up five hits, walked none and struck out five.
"We just couldn't generate any offense off him," Royals manager Ned Yost said. "He was good. We've been swinging the bats good but couldn't get anything going. He shut us down."
"I felt pretty good. I felt like I commanded my fastball pretty well," Giolito said. "I'd say that it was just on the mental side, feeling very comfortable pounding the strike zone because the defense from the get-go was just spectacular behind me today."
Outfielder Lorenzo Cain's fourth-inning home run was the Royals' lone run behind starter Ian Kennedy, who gave up seven hits and five runs over 5 1/3 innings.
"The [performance] didn't reflect what the stat line shows," Kennedy said. "I felt like my fastball was good. I made that one mistake with the slider, to [White Sox catcher Kevan] Smith. But just frustrating, because I felt better than the results."
MOMENTS THAT MATTERED Garcia goes oppo: Garcia got the White Sox going quickly in the first inning. After Yoan Moncada doubled with one out, Garcia hit a Kennedy fastball hard the other way, a two-run shot. The homer had a 107-mph exit velocity, according to Statcast™, with an estimated distance of 404 feet. It was Garcia's 18th home run this season and his three RBIs moved him to 80 overall for the first time in his career.
"We always set goals. We set goals and I'm grateful that God give me the opportunity to be who I am now," Garcia said. "I'm just thankful and I got to keep the same, the same routine, the same everything, and work hard every day, every year, every month so I can bring the best for my team."
Smith goes deep, too: White Sox catcher Kevan Smith ended a streak of nine consecutive batters retired by Kennedy when he took a breaking ball and drilled it into the left-field seats in the fourth inning. Statcast™ estimated that the ball traveled 411 feet. It was Smith's fourth home run this season and it gave the White Sox a 3-1 lead.
"I'd say that just the confidence and everything is right where it needs to be so I'm going to continue to try and pitch like I am."-- Giolito
WHAT'S NEXT Royals: Right-hander Jakob Junis (8-2, 4.05 ERA) takes the mound for the Royals in a makeup game at Yankee Stadium on Monday at 12:05 p.m. CT. Junis went 6 1/3 innings Wednesday and gave up two earned runs in a 15-5 win over Toronto.
White Sox: The final home series of the '17 season for the White Sox begins with James Shields (4-7, 5.40) on the mound with a 7:10 p.m. CT first pitch against the Angels Monday. Shields makes his 21st start of the season and 11th at home.