De Vries (4-5) yielded a single tally on seven hits, didn't issue a walk and struck out three en route to the victory.
Alex Burnett and Jared Burton combined for 1 1/3 scoreless relief frames and Glen Perkins turned a 1-2-3 ninth for his ninth save as Minnesota took the opener of a three-game series that had been washed out Friday.
Justin Morneau contributed a run-scoring double and a sacrifice fly in the victory.
Kansas City's Will Smith (4-7) was tagged with the loss, yielding three runs on nine hits over six frames.
Johnny Giavotella drove in the Royals' only run.