In his fourth start since his trade from Cincinnati, Cueto went eight innings, scattered eight hits, gave up one run, walked none and struck out four.
"I feel really good on this ballclub," he said through interpreter Pedro Grifol. "Every time I go out there, I feel I have a chance to win because the offense gives me runs and gives me that boost."
The Royals also give their pitchers great defense. Catcher Salvador Perez picked a runner off first, and center fielder Jarrod Dyson gunned down David Murphy at the plate as Murphy tried to score from second on a single.