Kinsler and Adrian Beltre both went 2-for-5 in the Rangers' second win in their last three tries.
Travis Blackley (0-1) took the loss for the A's, who lost for the 11th time in 13 games. Blackley allowed five runs on seven hits in 4 2/3 innings.
Yoenis Cespedes had a solo home run and Collin Cowgill had a two-run blast for Oakland.
Texas scored three runs in the third inning and led 5-0 by the time Oakland got on the board in the bottom of the fifth on Cowgill's first home run of the season.