Germany attacking midfielder Gotze had not played since being ruled out earlier this year for an indefinite time period because of "metabolic disturbances", but impressed as he played for just over an hour.
The 25-year-old made an early impact, teeing up American teenager Christian Pulisic who fired in from the edge of the box.
Dortmund, without France winger Ousmane Dembele amid interest from Barcelona, doubled their lead when centre-back Marc Bartra popped up on the left edge of Wolfsburg's penalty area, beautifully bending into the far top corner.
Eighteen-year-old Pulisic, who has been linked with a move to Liverpool, turned provider after the break when he drilled across the home goal for striker Pierre-Emerick Aubameyang to convert at the far post.
It was the perfect start for new manager Peter Bosz, who left Ajax to replace Thomas Tuchel earlier this summer.