KANSAS CITY, Missouri — Jarrod Dyson loves to boast about what speedy base runners can do.
"He knows he's got the ability to steal the tough base," Royals manager Ned Yost said.
Mike Moustakas doubled with one out in the ninth. Dyson ran for him and stole third and came around to score as Jake Petricka (1-5) threw a wild pitch.
After Nori Aoki doubled with two outs — for his fourth hit of the game — Gore, who was called up from the minors on Sept. 1 to primarily be a pinch runner, ran for him and scored from second on Lorenzo Cain's infield single.
"I was definitely going to be safe," Cain said. "I just put it in play and ran. They ended up bobbling the ball and Gore scored. I was definitely thinking he'd field it and hold on. (Cain is) fast. It's a huge win for the boys."
It was a bizarre ending to a game that the White Sox led 3-0 going into the seventh.
"It was strange," White Sox manager Robin Ventura said. "When you see a play like that you think that's OK, you can give it to them and try to get the next guy, but then they get another one. That kid (Gore) is fast. Speed can do a lot of things."
Wade Davis (9-2) worked a scoreless ninth to pick up the victory, extending his scoreless streak to 31 2-3 innings.
White Sox starter John Danks pitched six scoreless innings and allowed just two singles, both by Aoki, before departing after 103 pitches. He struck out six and walked four. Danks, who has a 1.73 ERA at Kauffman Stadium, has never lost to the Royals in 15 career starts.
The Royals scored all their runs off three White Sox relievers.
Royals right-hander James Shields, who had his career best 18 1-3 scoreless innings streak ended in the first, gave up three runs and 10 hits, while striking out six and walking none in seven innings.
"We had a lot of opportunities, but he came through," Ventura said. "We never got the big hit to put it out of reach. He was tough."
Avisail Garcia's two-out single in the first scored Adam Eaton. Eaton, who had three hits, led off the White Sox third with a double and scored on a Shields' wild pitch. Conor Gillaspie singled home Alexei Ramirez with the second run of the inning.
Eric Hosmer hit a double into shallow left off Javy Guerra to open the seventh and scored on Omar Infante's single for the first Kansas City run.
Aoki led off the eighth with an infield single, advanced to second on Gillaspie's throwing error, took third on a Zach Putnam's wild pitch and scored on Alex Gordon's single.
AOKI'S BIG NIGHT
Aoki's four hits, two that did not leave the infield, matched his career high, last accomplished on Sept. 20, 2013, against St. Louis. He also walked, reaching base five times. Aoki, who swings left-handed, is hitting .360 against left-handed pitching. It was his fourth multi-hit game in his past eight games.
White Sox: RHP Chris Bassitt will make his fourth career appearance and third big league start Tuesday. Bassitt has allowed 14 hits, walked seven and hit two batters in 13 1-3 innings.
Royals: RHP Liam Hendriks, who retired only seven of the 15 batters he faced in a loss Thursday to Boston, will make another spot start Tuesday.
White Sox: DH-1B Paul Konerko (fractured left hand) took batting practice and could return to the lineup this week.
Royals: LHP Danny Duffy (sore shoulder) will miss another start. He is scheduled to throw a 50-pitch four-inning simulated game Tuesday. If he has no problems, he will start Monday at Cleveland. . DH-OF Josh Willingham (groin strain) said he is available to pinch hit. He has trouble running, but not swinging.