Oakland was playing its last game in Arizona before leaving for Tokyo, where the A's meet Seattle in an opening two-game series next Wednesday and Thursday.
Lorenzo Cain hit his third home run, and Alex Gordon and Eric Hosmer each had two hits and drove in a run for the Royals, who won for the fifth time in six games.
A's starter Graham Godfrey threw only 37 of 75 pitches for strike. He gave up three runs, six hits and two walks in three innings. Minor leaguer Cedric Hunter homered for the A's.