Betemit's two-run homer in the third inning was part of a 12-hit Royals attack that posted all 11 runs in the first three innings.
The outburst gave Greinke (9-12) the support he needed for his first victory since Aug. 17. The 2009 Cy Young Award honoree held Oakland to three runs on six hits in seven innings.
Oakland loaded the bases in the first inning but did not score their first run until sixth inning when Landon Powell and Jack Cust hit back-to-back RBI singles and Akinori Iwamura drove in another run on a groundout.
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