The Rangers captured the opener of the twin bill 6-3 and the sweep gives them three victories in a row.
Oakland took a 1-0 lead in the first, just as it did in the first game, but the Rangers quickly rallied and stayed in front thanks to a solid pitching effort.
Josh Hamilton doubled home Ian Kinsler with the initial run in the Texas first, Nelson Cruz followed with a single and Hank Blalock doubled to left, scoring Hamilton.
After Chris Davis was intentionally walked to load the bases, Teagarden singled on the first pitch from Edgar Gonzalez (0-1).
Scott Feldman (4-0) got the win by surviving six innings. He allowed two runs on five hits.
C.J. Wilson, who was credited with the win in relief when the Rangers scored three times in the eighth inning of the first game, got his fourth save in the second contest.