Moncada was 3 for 3 with a walk and three runs scored a day after leaving a game with a bruised right knee. Palka also had three hits and two RBIs while Tim Anderson and Kevan Smith each hit a two-run double as Chicago pounded out 13 hits.
Adalberto Mondesi homered leading off the eighth for the Royals, who are 2-11 in July.
In the final game before the All-Star break, Kansas City decided to go with a bullpen day. The relievers were no match for Giolito (6-8). The right-hander allowed just two hits in 6 1/3 innings, striking out six and walking three.
After Giolito worked out of his only jam in the top of the first with an assist from the defense — Jorge Bonifacio was thrown out trying to score from second on a single to left with one out — Palka's two-run blast off starter Burch Smith (0-1) gave the White Sox a 2-0 lead.
The lead grew to 4-0 in the third as Abreu scored on a wild pitch and Leury Garcia followed with an RBI single against left-hander Brian Flynn. Chicago then broke the game open with a five-run fifth against left-hander Enny Romero. Moncada, who was hit in the knee by a pick-off throw on Saturday, started things with a lead-off homer. Anderson and Smith each had a two-run double to make it 9-0.
Moncada doubled and scored in the sixth to make 10-0 before Mondesi's homer off Jeanmar Gomez broke the shutout.
TRAINER'S ROOM
White Sox: RHP Nate Jones (strained forearm muscle) will travel to Triple-A Charlotte during the All-Star break and throw live batting practice on Tuesday.
UP NEXT
Royals: LHP Danny Duffy (4-8, 4.59 ERA) will pitch the opener of a three-game series with Minnesota on Friday night.
White Sox: RHP James Shields (4-10, 4.43 ERA) takes the mound Friday night for the start of a three-game series at Seattle.
