Gonzalez, a candidate to replace the injured Yu Darvish in the Rangers' rotation, threw 58 pitches and allowed two hits, three walks and struck out three.
Odor homered in the third off A's right-hander Jesse Hahn. Prince Fielder, who homered and drove in three runs Sunday against Cleveland, added another RBI with a rare infield single in the fifth.
Chris Gimenez drilled a two-run single off Eury De La Rosa in the sixth to cap off the Texas scoring.
Hahn, who is competing for a job in the A's rotation, gave up a run on three hits, while walking one and striking out two. The A's avoided a shutout when Matt Olson homered in the eighth.
The A's loaded the bases with none out in the ninth, but failed to score off minor leaguers Mark Rogers and Kohsuke Tomita.