The Rangers have won two out of three in the four-game series to slow down a slide that had seen them fall out of first place in the American League West.
Texas came into the series on a six-game losing streak, during which the Rangers had managed a total of eight runs. They have scored 17 runs in their two wins over the Athletics.
Chris Young hit a three-run homer for Oakland in the fifth that gave the Athletics a 3-2 lead, but Texas then produced seven runs over its next three innings to break things open.
The Rangers cranked out 14 hits and took the lead for good in the fifth when Leonys Martin scored on a fielder's choice grounder off the bat of Nelson Cruz.
Martin then singled in the first run in the Texas sixth, after which the Rangers scored on singles by Ian Kinsler and Cruz and the double by Beltre.
The offensive show made a winner out of Justin Grimm (6-5), who gave up three runs on three hits in five innings.
Tommy Milone (6-7) was roughed up for six runs on eight hits in 5 1/3 to take the loss.