Tampa Bay pitcher David Price finally managed to get the better of Texas as the Rays became the first team to register a series victory over the Rangers this season with a 5-2 triumph on Sunday.
Price entered the contest with a 0-6 record against the Rangers but allowed just two runs over 6 1/3 innings to seize a maiden win against the American League leaders.
Tampa Bay scored three runs in the second inning and took a 4-1 lead in the third but the Rangers made life difficult for the visitors when they loaded the bases in the ninth, before closer Fernando Rodney dug deep to record the final out.
Ian Kinsler hit a weak, game-ending line drive back to Rodney, who recorded his seventh save of the season and helped the streaking Rays take two wins from Texas in the three-game set.
Josh Hamilton hit an RBI single for the Rangers (16-6) in the first but was forced to leave the game shortly after because of stiffness in his back.
Ben Zobrist finished 3-for-4 with an RBI for Tampa Bay (14-8), who have won seven of their last eight games.
(Writing by Jahmal Corner in Los Angeles; Editing by John O'Brien)