Left-hander Jonathan Sanchez kept the Giants close with a strong performance in his third Cactus League start, allowing a run and two hits and striking out five in four innings.
The teams played each other for the first time since last year's World Series, won by San Francisco in five games.
Former Giant Yorvit Torrealba doubled in a run in the second inning for the Rangers. Alexi Ogando, a reliever in 2010 making his first spring training start, struck out four in three shutout innings for Texas.
The Giants scored all of their runs off reliever Tommy Hunter, who gave up five hits and struck out three in three innings.