Garrett Richards (6-6) controlled the Rangers on two runs (one earned) on six hits over seven innings, walking one and striking out five.
Rangers starter Derek Holland (9-8) was pounded for eight runs (four earned) on eight hits in a 5 2/3-inning performance.
A.J. Pierzynski homered for second-place Texas, which fell 1 1/2 games behind American League West-leading Oakland with their sixth loss in eight games.
The Rangers hold a three-game lead over Tampa Bay for the first AL wild card spot.
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