The Tigers have lost two in a row and dropped three games behind the Chicago White Sox in the battle for the American League Central title.
Chen (10-10) struck out four and walked only one while throwing 100 pitches.
Greg Holland came on in the ninth for the Royals and promptly put runners on first and second with one away. He then struck out Delmon Young and Jhonny Peralta swinging to end the game and collect his ninth save.
The game's only run scored on a bloop infield hit by Eric Hosmer in the fourth inning.
Anibal Sanchez (2-4) took the hard-luck loss, giving up a run on seven hits without a walk in seven innings.
Costly malfunction causes beer flood at Boston-area brewery
Megyn Kelly: Santa Claus and Jesus are both white men