Butler's two-run homer in the third inning handed the Royals a 3-0 lead and his sacrifice fly in the fifth put them up by six.
Mike Moustakas went 2-for-4 with a solo homer and three runs scored for the Royals, who rebounded from a 6-4 loss in the opener of their three-game interleague set.
Chen (3-4) won his third consecutive start, allowing a pair of runs on eight hits over 6 1/3 innings. The left-hander walked two and struck out four.
Diamondbacks starter Ian Kennedy (3-4) was roughed up for six runs on eight hits, lasting only 4 1/3 frames.