Right fielder Nori Aoki prevented the White Sox from taking a lead when he made a lunging catch of Alexei Ramirez line drive to end the eighth with two runners on base.
Conor Gillaspie hit an RBI single in the eighth before Paul Konerko's sacrifice fly tied it and gave him 146 RBIs against Kansas City, the most by any opponent.
Royals left-hander Bruce Chen allowed one unearned run on six singles, walked none and struck out seven in 6 1-3 innings, but had to settle for a no-decision.
"Chen and John are guys that are crafty," White Sox manager Robin Ventura said. "They're uncomfortable for guys to hit, but I thought our guys battled back. We feel like we can fight back."
Moustakas' fielding error led to an unearned White Sox run in the fifth. Adam Eaton's groundout scored Ramirez.
NOTES: The Royals designated for assignment IF Pedro Ciriaco, who has a .277 career batting average in the majors with four clubs, and purchased the contract of RHP Aaron Brooks from Triple-A Omaha. With the addition of Brooks, the Royals have a 12-man pitching staff. Brooks, who was a starter in the minors, will go to the bullpen. . The White Sox have lost their first two away games after going an AL worst 26-55 in road games last year. . White Sox RF Avisail Garcia, in an 0-for-13 funk, was given the day off. . Aces LHP Chris Sale of the White Sox and RHP James Shields of the Royals are set to pitch Sunday.