Davies didn't waver until the eighth, when he took the mound with a 5-0 lead. Jim Thome led off with a walk and Alexei Ramirez homered to left-center on Davies' 101st pitch of the game. The right-hander left afterward, allowing just three hits.
"We've seen it back-to-back," Royals manager Trey Hillman said of Davies. "He's so locked in right now. The recipe was pretty much the same. He has gotten to the point where he realizes he has the ability to let every pitch go with max effort. Hopefully, he'll do it again and finish off the season strong."
Davies faced the minimum through seven innings, using double plays in the first and second innings to keep his pitch count in order.
"It's the tempo and the mindset on the mound that has changed the whole thing," Davies said. "It's not about trying to hit corners. It's about getting my best stuff to home plate and let's see what happens."
The Royals hitters did their part, giving Davies some early runs to work with. Against a 16-game winner in Gavin Floyd, the Royals beat the White Sox at their own game. The White Sox often win with a homer-happy offense, but this time it was Kansas City getting three homers. One of those was an inside-the-park homer by David DeJesus.
The Royals jumped on top in the third when Alex Gordon launched a two-run homer to left-center. It was the 15th homer for Gordon and Hillman could recall only a couple of balls hit to the opposite field and out, before the left-handed-hitting Gordon showed power going the other way on Saturday.
In the fourth, DeJesus hit a long drive down the right-field line and right fielder Jermaine Dye banged into the wall and fell, while giving chase. The ball rolled far enough away for DeJesus to circle the bases.
Then, in the seventh, rookie Kila Ka'aihue showed the power that characterized his summer against Double-A and Triple-A pitching. Ka'aihue hit a towering homer to right for a 4-0 advantage and an RBI single by Mike Aviles made it even more comfortable for the Royals.
The White Sox didn't go easily, however.
After Ramirez hit his two-run homer in the eighth, the White Sox put two on in the ninth against All-Star closer Joakim Soria. Dye made a bid for a game-tying, three-run homer but Mark Teahen used a mini-hop to make the catch just in front of the wall.
"I didn't think [Dye] got it, but honestly, I didn't think Alexei got his and that ball went out," Hillman said. "When Dye hit it, I was just hopeful."
Soria took a deep breath and fanned Jim Thome with a two-strike offspeed pitch that earned Soria his 41st save.
Kansas City (70-85) surpassed last year's win total with seven games remaining. It's the most victories for the Royals since they finished 83-79 in 2003.
Davies will get one more shot next weekend in Minnesota to build on his late-season momentum.
"He's letting his pitches go with a little more authority and staying balanced a little longer," Hillman said. "When you locate and have more confidence, you're going to let go of your pitches with a little more conviction."