Dortmund's coach Jurgen Klopp conceded his team lacked 'freshness' in their ninth game in 32 days, while captain Sebastian Kehl declared they 'definitely got lucky' as Wolfsburg took 27 shots to the home side's nine at Signal Iduna Park.
Henrikh Mkhitaryan and Robert Lewandowski scored the goals for Dortmund in the first half but the result could have been much different if Wolfsburg had taken their chances away from home.
The visitors almost equalised just before Lewandowski's goal when Junior Malanda's header struck the post and Kevin De Bruyne missed the rebound.
Malanda also wasted two fine chances for the visitors after half-time, with Dortmund goalkeeper Roman Weidenfeller producing a brilliant double save on the second opportunity, blocking the defensive midfielder's close-range effort and then tipping Luis Gustavo's follow-up shot onto the post.
The victory was similar to Dortmund's win over Wolfsburg in the Bundesliga on April 5 when the North Rhine-Westphalia club had to come from behind to triumph 2-1.
"Despite the 2-0 that was very close," Dortmund defender Mats Hummels said after the DFB Pokal semi-final.
"We were lucky that Wolfsburg (struggled to hit the back of the net). They had really good chances.
"One must conclude honestly that Wolfsburg in the last two games against us really had a lot of bad luck. We are glad that we made it to the final. "
Kehl agreed: "If you look at it objectively, you have to realise very clearly that we definitely got lucky in one way or another.
"Wolfsburg (created) a lot of chances but for whatever reason were unable to score a goal."
Klopp argued his team looked tired for the first time in a month after impressive wins over Real Madrid and Bayern Munich in their past two matches.
"We have made the finals, all is well. With the quality that Wolfsburg have, it is normal that they have chances," he said.
"The boys have played a lot of football and today it has taken its toll for the first time.Wolfsburg always stayed focused and we had our chances on the break but we played rather average due to lack of freshness."
Wolfsburg coach Dieter Hecking praised his team but admitted the difference between the two sides was their 'coolness in front of goal'.
"I'm proud of my team, who made a great game. I even believe that we were the better team in certain stages of the game," Hecking said.
"The difference you have also seen. The coolness in front of goal that Dortmund had, was missing (for Wolfsburg)."
