The Royals lost for the 13th time in 15 games.
Giolito (6-8), a right-hander, allowed two hits, walked three and struck out six as he improved to 3-0 in his career against the Royals. It was his first scoreless start of the season and his best at home, as he entered the game at 2-4 with an 8.65 ERA at Guaranteed Rate Field.
It didn't take long for the White Sox's offense to get going against a Kansas City pitching staff that was using a bullpen-by-committee approach in the final game before the All-Star break.
Royals right-hander Burch Smith (0-1) surrendered a two-run homer to Palka in the first inning and the rout was on. Moncada led off with a single and, two outs later, Palka lined a 2-0 pitch over the wall in right-center field, his 12th homer of the season.
Chicago added two runs in the third off left-hander Brian Flynn, one scoring on a wild pitch and the other on a Leury Garcia single.
The White Sox pulled away with a five-run fifth off left-hander Enny Romero, sparked by Moncada's leadoff homer, his 12th, to left-center field. With two outs, singles by Palka, Garcia and Matt Davidson loaded the bases. Tim Anderson and Kevan Smith each hit two-run doubles to give Chicago a 9-0 lead.
Moncada led off the sixth with a double off right-hander Jason Adam and advanced to third on a fielding error by right fielder Jorge Bonifacio. Moncada scored on Yolmer Sanchez's single as the White Sox took a 10-run advantage.
The Royals' Adalberto Mondesi homered, his third, leading off the eighth inning against right-hander Jeanmar Gomez to spoil Chicago's shutout bid.
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