Texas scored all its runs in the fourth inning, with a two-run blast by Adrian Beltre putting the Rangers in front.
Darvish (6-1) gave up a first-inning run and four hits. His ERA dipped to 2.60 and he has fanned 58 in 52 innings this season.
Josh Hamilton reached on an infield single in the fourth and scored on Beltre's homer. Hamilton had two hits overall, extended his hitting streak to 16 games and his batting average advanced to .410.
The loss went to Tommy Milone (5-3), who gave up four runs on nine hits in seven innings.
Celebrity Families of 2014 [PHOTOS]