Henrikh Mkhitaryan opened the scoring before the Poland international brought up three figures for the club to keep alive their last remaining hope of silverware this season
Henrikh Mkhitaryan opened the scoring for Dortmund, just as he did in the weekend victory over Bayern Munich, as he expertly fired home from the edge of the penalty area after 13 minutes.
The visitors had plenty of possession and opportunities, but Lewandowski killed their momentum with his to bring up a century of Dortmund goals on the stroke of half-time.
Despite a flurry of late chances, there was to be no comeback as Dortmund beat Wolfsburg at home for the second time this month to set up a meeting with either Kaiserslautern or Bayern in the final on May 17.
Wolfsburg made the stronger start and thought they had taken the lead just two minutes in when former Dortmund man Ivan Perisic headed home before play was brought back for a foul on Roman Weidenfeller.
Dortmund's first sight of goal came soon after with an audacious Marco Reus backheel that was easily collected by Florian Grun. But they did not have to wait too much longer before taking the lead as Mkhitaryan produced a finish of the highest quality.
After Lewandowski played in Reus, the German pulled the ball back for Mkhitaryan to finish left-footed from 20 yards.
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 went close again 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.
Reus played in the Pole and, with the visiting defence stretched, he angled a finish into the top left-hand corner to put the hosts in sight of Berlin.
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.
The Belgian was also denied in a frantic late goalmouth scramble as Dortmund became the first team since Eintracht Braunschweig in October to keep a clean sheet against Wolfsburg and maintain their hopes of a fourth Pokal crown.