Bruce Chen gave up one run and five hits in 5.2 innings and was spotted an early 3-0 lead as the Royals swept the Twins and grabbed their fifth straight win, a 3-1 final.
The Royals outscored Minnesota 17-3 in the three-game set to finish the season series with a 15-4 record against their AL Central rival. Kansas City has won seven straight at Target Field.
Kelvin Herrera and Will Smith combined for 2.1 innings of scoreless relief. Greg Holland pitched a scoreless ninth for his 36th save in 38 chances.
Chris Getz, Alcides Escobar and Alex Gordon singled home runs in the second.