Darvish, 93-38 with a 1.99 ERA in 167 games in Japan's Pacific League the past seven seasons, got out of the second when Michael Saunders took a called third strike. Darvish then got on a roll in the third before the Rangers' big bats put him in the lead.
Cruz, the ALCS MVP last October, got his first homer of the season when he pulled a liner into the left-field seats right after Hamilton was called out at home trying to score on Young's grounder.
Hamilton argued briefly with home plate umpire Paul Nauert, and replays showed that the slugger might have slid around catcher Olivo's tag.
There was no doubt about Hamilton scoring in the fourth, his second homer of the season a solo shot over the center-field wall off rookie right-hander Erasmo Ramirez.
That was the only run allowed in three innings by Ramirez in his major league debut.
Notes: Ogando, a 13-game winner and All-Star as a starter last season, went 1 1-3 innings. He has appeared in three of four games, with 3 1-3 scoreless innings. ... Neftali Feliz, the Rangers' closer-turned-starter, makes his first start Tuesday night against Seattle. He faces right-hander Blake Beaven, the former top prospect for the Rangers who was traded to Seattle two seasons ago in the Cliff Lee deal.
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