Jarrod Dyson hit his first career homer and Josh Fields added a two-run shot for the Royals, who opened a three-game series at Kauffman Stadium with a victory.
Former Twin Philip Humber (2-1) collected the victory with 2 2/3 innings of one-run relief. Joakim Soria notched his 42nd save with a scoreless ninth.
Jeff Manship (2-1), the second of seven Minnesota pitchers, was tagged with the loss after blowing an 8-7 lead in the fourth inning.
Jason Kubel clubbed a three-run homer and drove in a total of five runs for the American League Central champion Twins, who dropped their fourth straight game.