Mike Moustakas finished 3 for 3 and knocked in the other run in the deciding frame for the Royals.
Donnie Joseph picked up the win by recording the final two outs of the fifth in relief of Yordano Ventura. Ventura fanned six and gave up a run on two hits over 4 1/3 innings.
Billy Burns walked twice and knocked in the lone run for the Athletics. Sean Doolittle was charged with all three runs in the sixth in defeat.