Darvish (8-3) allowed four hits in recording his first win since May 16, a span of eight starts. The right-hander overcame four walks and struck out eight.
He left with a 3-0 lead but the Rangers' bullpen faltered in the eighth inning.
Joe Nathan then turned in a 1-2-3 ninth for his 27th save as the American League West-leading Rangers recorded their ninth victory in 11 games.
Reds starter Mat Latos (7-2) was hung with the loss after yielding three runs (two earned) on eight hits over 6 2/3 frames.
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