Texas avoided being swept by Oakland and is only one of two teams along with the Yankees without three straight losses.
The 30 year-old right-hander received a standing ovation from the crowd after giving up three hits and striking out two.
In the first inning, Rangers left-fielder David Murphy gave Wolf an early cushion with a two-run home run that scored Elvis Andrus. Two batters later, Adrian Beltre’s solo shot to center field made the score 3-0.
The A’s got on the board in the fourth inning on Brandon Moss’ sacrifice fly to score Coco Crisp.
With runners on first and second in the sixth, Texas left handed reliever Neal Cotts struck out the side to escape the inning. He allowed one hit and zero earned runs over the sixth and seventh innings.
Rangers closer Joe Nathan struck out A’s catcher Derek Norris to earn his 14th save of the season.