Duensing (3-5) scattered six hits and a walk in his 113-pitch effort, during which only one Royals runner reached as far as third base. He struck out four.
The Minnesota left-hander notched his first victory since April 23, a span of eight starts, as the Twins registered their first four-game sweep of the Royals since April 2006 while outscoring them 26-6.
Jason Repko drove in three runs with a pair of singles and Matt Tolbert added a two-run triple in Minnesota's win.
Jeff Francis (2-6) absorbed the loss, allowing four runs (one earned) on six hits in a seven-inning start for Kansas City.