The Rangers won their third in a row and have captured 11 of their last 13 contests.
Texas overcame a 4-2 deficit with a four-run fifth, highlighted by David Murphy's two-run single. Murphy has six hits and seven RBI over his last two games.
With the Rangers clinging to a one-run lead heading into the ninth, Nathan retired the first batter of the inning.
Josh Reddick then drew a four-pitch walk, went to second on a wild pitch and stopped at third when Yoenis Cespedes singled to right.
Nathan survived the trouble, however, striking out Seth Smith and getting Brandon Inge on a grounder to shortstop. It was Nathan's 18th save.
Scott Feldman (2-6) was credited the win after a struggling, five-inning performance. He gave up four runs on nine hits.
Tyson Ross (2-8) surrendered five runs on eight hits in four frames to take the loss.
Josh Reddick, Derek Norris and Cliff Pennington all hit solo homers for the A's.