Miley (5-1) allowed three runners to reach third base but pitched out of trouble each time, scattering six hits and a pair of walks while striking out three.
The rookie left-hander won his second start in a row, lowering his ERA 2.14.
Royals starter Nate Adcock (0-2) absorbed the hard-luck loss, yielding one run on five hits over five frames.
Jeff Francoeur went 4-for-4 for Kansas City.
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