CHICAGO -- Danny Duffy couldn't help but think about his last start at U.S. Cellular Field.
His previous outing in Chicago didn't go well at all. Duffy injured his elbow in the first inning on May 13, 2012. Soon after he had Tommy John surgery and missed about a year.
"I've been waiting to come back here for a long time," Duffy said. "It's just nice to come out and do my job in this city and in this setting."
The victory was the sixth straight for the Royals while the White Sox dropped their ninth in 10 games against Kansas City.
Royals manager Ned Yost said there was a lot to like about Duffy's complete effort.
"For four innings he was really efficient, he really kept his pitch count down," Yost said. "He had everything working: his fastball, his breaking ball, had a good changeup and had a really, really good defense behind him."
Mike Moustakas homered among his three hits as the Royals won their second straight in this weekend series.
The Royals scored five times in the fourth -- four with none out -- to chase Chicago starter Hector Noesi (2-5).
Noesi allowed five runs -- two earned -- and eight hits while walking one and striking out four.
"To be able to put five runs on the board was big," Yost said. "We've and a couple of big innings the last week or 10 days. Early in the year we get something going we get one or two out of it. Now that we're swinging the bats better we're getting four or five."
Duffy last struck out nine on June 19, 2011, at St. Louis. He's now 2-0 against Chicago.
Duffy departed in the eighth inning after a leadoff single by Adam Eaton.
Two runs scored in the five-run fourth when third baseman Leury Garcia bobbled Lorenzo Cain's grounder for an error.
Moustakas then singled to shallow center for another run.
Alcides Escobar's base hit extended his hitting streak to a career-high 12 games and loaded the bases for the second time in the inning.
The Royals' fourth run came on Nori Aoki's double-play grounder. Omar Infante lined a two-out single to left, driving in Moustakas for a 5-0 lead.
Noesi was chased in favor of right-hander reliever Javy Guerra with two outs in the fourth.
"Hector, he's been good for us and he's always given us a chance, but we have to help him out on occasion," White Sox manager Robin Ventura said. "If we're not helping him on defense, it's going to make a difference. That's a recipe to lose a game in a hurry."
Moustakas' homer in the eighth inning was his sixth of the season. He finished with two RBIs and two runs scored.
Eric Hosmer had an RBI double to left to start a three-run ninth. Butler's one-out homer to right made it 9-0.
Despite giving up an eighth inning single to Eaton, Duffy's shutout was preserved after Eaton was thrown out at home on a throw by Aoki in a play overturned following a review.
Escobar was in Saturday's lineup despite having cramps and leaving Friday's game after extending his hitting streak to a career-high 11 games with a ninth inning double.. Kansas City has scored first in each game of its current six-game winning streak.. Royals right-hander James Shields (7-3, 3.44 ERA) makes his 15th start of the season in Sunday's series finale against White Sox right-hander Andre Rienzo (4-3, 5.25 ERA), making his 11th start.. After going 63-99 in 2013, Ventura is pleased to have his team in contention this year, but he won't project beyond Saturday. "We're not going to look that far down the road," he said. "We're better off focusing on what we're doing today."