Kubel's big night at the plate backed Kevin Slowey (7-3), who allowed just three hits, did not issue a walk and struck out three.
Matt Guerrier came on to record the final out in the ninth with two runners on to notch his first save of the year.
Cy Young Award winner Zack Greinke (1-8) continued to struggle, giving up six runs on nine hits. Kansas City has failed to score for him in his last 22 innings.
The Royals dropped their fourth game in six contests.
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