Scott Sizemore hit a pinch-hit, go-ahead run sixth inning, as the Athletics downed the 7, in the middle contest of a three-game series.
Trevor Cahill (11-13) lasted five-plus innings, allowing five runs on seven hits to earn the win. He walked two and struck out three.
Ryan Sweeney went 2-for-4 with a triple, two runs scored and two RBI for the A's, who had lost three of their previous four.
Alexi Ogando (12-8), in his first start since August 31, allowed five runs -- three earned -- over five-plus innings to suffer the loss.
Adrian Beltre hit a two-run homer for the Rangers but lined out with runners on first and second in the bottom of the ninth, securing Andrew Bailey's 20th save of the season.
The Rangers lead the AL West by 1 1/2 games over the Angels.
The Rangers, who won the series-opener 13-4 on Friday, opted to skip Ogando's last start in order to rest the slumping righty. The results were not ideal, as Sweeney belted a two-run triple and Kurt Suzuki followed with a sac fly two batters later to give the A's a 3-0 lead in the second.
In the home third, Ian Kinsler singled with two outs and Elvis Andrus doubled before Cahill's wild pitch allowed the Rangers to get on the board. An inning later, Mitch Moreland's two-run double tied the game.
Both pitchers faced the minimum in the fifth, but Ogando hit Josh Willingham and allowed a David DeJesus single to begin the sixth, marking the end of his outing. Michael Gonzalez recorded two outs before walking Suzuki to load the bases. Sizemore then ripped a 1-0 fastball from Yoshinori Tateyama over the wall in left for his first career grand slam. Cliff Pennington's RBI double later in the frame made it an 8-3 game.
"It was awesome," said Sizemore. "That was my first big league grand slam. To be a pinch-hit one and to give us the lead, that was even more special."
The Rangers persisted, however, beginning with Beltre's two-run homer in the bottom of the sixth, which chased Cahill. Brian Fuentes entered and allowed David Murphy to reach third before ending the inning.
Fautino De Los Santos began the home seventh for the A's and allowed a two-run single to Michael Young before giving way to Grant Balfour, who ended the inning unscathed before tossing a scoreless eighth.
In the ninth, Bailey walked Josh Hamilton and allowed a Young single with two down before lining out Beltre to end the game.
"It's just the way it works sometimes," said Moreland. "You're gonna hit some balls hard and make outs. You have to credit them for making the defensive plays to keep it in their hands."
Cahill has won two straight starts for the first time since June 19-25...Ogando has not won since August 15 and has dropped each of his last three starts...The Rangers saw their win streak over the A's end at nine games.