Jason Repko drove in three runs off starter Jeff Francis, and Matt Tolbert hit a two-run triple in the ninth off Jesse Chavez in a 7-0 loss for the Royals.
The last time the Twins swept four from Kansas City was Aug. 3-6, 2006.
Brian Duensing (3-5) gave up six hits with one walk and four strikeouts in his longest outing of the season.