Mike Moustakas started the frame with a single to right and moved to second on a sacrifice bunt. Aoki singled on a soft line drive, but Sox center fielder Adam Eaton threw a strike from center as Moustakas rounded third. The ball beat Moustakas home, but he was able to knock it loose from catcher Tyler Flowers' glove as he slid into the plate.
Greg Holland retired the side in order in the ninth to register his 26th save.
Shields, who was going for his fourth straight win at U.S. Cellular Field, gave up one run and six hits while striking out seven, but received a no decision.
Wade Davis (6-2) pitched a perfect eighth inning for the Royals, who have won their fourth consecutive series on Chicago's home field.
Zach Putnam (2-1) gave up two hits and the deciding run in the ninth for the loss.
Jose Quintana started for the White Sox and went seven innings, only allowing one run and scattering seven hits, but received his fourth straight no decision.