Rookie left hander Danny Duffy (2-4) collected his first win at Kauffman Stadium, giving up seven hits and two earned runs but striking out six. Chicago's Jake Peavy (4-4) took the loss, his fourth of the season.
The damage came on the bat of Matt Treanor. Just a little blooper was all they needed to score Billy Butler and Jeff Franceour.
The Royals slipped to their lowest point of the season Monday night, falling 20 games below .500. after their 5-2 loss to the White Sox Monday night.
Bruce Chen gets the start Wednesday night to wrap the series.