Gentry came home on an error by Angels starter Garrett Richards in the second inning, putting the Rangers ahead to stay at 2-1, and capped the scoring with an RBI bunt single in the fifth.
Texas scored four runs in the second, scoring twice on Angels miscues and once on a Richards wild pitch, taking a 5-1 advantage.
Alex Rios and A.J. Pierzynski each knocked in a run for the surging Rangers, who came into the contest one game behind American League wild-card co-leaders Tampa Bay and Cleveland with one game to play.
Richards (7-8) was tagged for six runs (three earned) on six hits over 4 1/3 innings.
Mike Trout drove in a pair of runs for the Angels.
Theater accidentally screens 'Nymphomaniac' trailer instead of Disney's 'Frozen'
18-year-old elf alleges mall Santa pinched her buttocks on the job