Wolf (1-0) was pulled after five innings but only allowed three hits and two walks while striking out three.
The Rangers' offense spotted Wolf to a 3-0 lead in the first to beat Jarrod Parker (2-6).
Elvis Andrus led off with a single and two pitches later David Murphy drove a Parker offering into the right-field seats. After an out, Adrian Beltre hit a smash to straightaway center for his 10th home run of the season.
Parker has allowed 11 home runs this season.
The Oakland run came in the fourth when Wolf allowed two hits and a sacrifice fly to Brandon Moss.