Loe was replaced by Veras, who threw only one pitch in the strike zone before issuing the decisive walk to Moustakas.
Kansas City forced extra innings by scoring twice in the ninth, both runs coming in on a triple by Alcides Escobar.
The Royals' ninth-inning rally spoiled a seven-inning, one-run performance by Milwaukee starter Randy Wolf.
Tim Collins (3-0), the sixth Kansas City pitcher, grabbed the victory by working the top of the 11th.
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