Jake Brentz (3-2) was the winner. Wade Davis finished for his second save of the season after Greg Holland gave up two runs in the ninth.
Kyle Funkhouser (4-1) allowed all five runs in the seventh for Detroit.
The Tigers pounced on Carlos Hernández early, backed by Jeimer Candelario and Miguel Cabrera. Hernández gave up five runs, four earned, on two hits with four walks in 2 2/3 innings with two strikeouts.
A three-run home run by Candelario in the third gave Casey Mize a comfortable lead.
Mize struck out six in 4 2/3 innings but gave up four runs on six hits with a walk.
Akil Baddoo hit a two-run homer in the ninth for the Tigers, his ninth of the season and fourth in the last 11 games.
Tarik Skubal (6-8, 4.18 ERA) will take the mound for Detroit in the series finale. Daniel Lynch (0-2, 15.75 ERA) will make his fourth career start for Kansas City.