The hit came off Wade Miley (8-3), who until Gentry's single had limited the Rangers to two hits while striking out eight.
Texas starter Matt Harrison did not figure in the decision after throwing 7 1/3 shutout innings. Harrison has gone six straight starts without a loss.
Miley walked Mike Napoli to open the eighth inning, the first base on balls he had allowed in 93 batters.
That brought up Gentry, who hit a sharp grounder on a 1-0 pitch that bounced up and off the glove of third baseman Ryan Roberts. Napoli beat the throw home, after which an obviously upset Miley was removed from the game.
The victory went to Mike Adams (1-2), who replaced Harrison with a runner on second and one away in the eighth and worked out of the jam. Joe Nathan struck out two in a perfect ninth for his 13th save.
Texas won its third in a row. Arizona has dropped two straight on the heels of a five-game winning streak.
The Rangers have held the Diamondbacks to one run over the first two games of the series.
2014: The Year in Music [PHOTOS]