Hillenbrand drove in three runs while going three for five with a two-run homer.
Cormier made his third start for the Diamondbacks and gave up three runs on eight hits in six innings. Greg Aquino, who recently inherited the role of closer, earned his second save.
Arizona won for just the second time in 18 games.
The loss went to Tim Redding (4-7), who surrendered six runs on nine hits over 5 2/3.
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