Jurgen Klopp's men beat Real Madrid 2-0 in the UEFA Champions League seven days prior to their semi-final against Dieter Hecking's side.
While that win failed to keep Dortmund in the competition, the momentum helped them comfortably beat Bundesliga champions Bayern Munich on Saturday before they kept their hopes of silverware alive at Signal Iduna Park.
The visitors had plenty of possession and opportunities, but Robert Lewandowski ended their momentum with his 100th Dortmund goal on the stroke of half-time.
Dortmund's first sight of goal came soon after with an audacious Marco Reus backheel that was easily collected by Florian Grun, although they did not have to wait too much longer to go ahead as Mkhitaryan produced a finish of the highest quality.
But for a poor final touch Reus would have found himself through on goal soon after and Wolfsburg's Kevin De Bruyne forced a save from Weidenfeller before the Belgian's teasing set-piece delivery evaded his team-mates in the penalty area.
They came closest however when Junior Malanda's header hit the post - with De Bruyne putting the rebound - wide and Lewandowski made them pay with a cool finish after a swift Dortmund break.
Wolfsburg could have made the ideal start to the second half when Ivica Olic pressured Weidenfeller into a poor punch, only for Maximilian Arnold to divert an effort wide.
Lewandowski's header was then ruled out for offside before Malanda skied a gilt-edged chance from close range.
