Ogando (3-2) yielded one run on six hits and two walks while striking out four in notching his first victory since April 8.
Gentry's RBI single in the fourth inning broke a 1-1 tie and he later iced the victory with a two-run homer in the eighth as Texas clinched its three-game series.
Ian Kinsler also went deep for the Rangers.
Red Sox starter John Lackey (1-2) was touched for three runs on six hits over five full frames.
Daniel Nava drove in the only run for Boston.