A 25th-minute goal from Antonio da Silva was enough for Armin Veh's side to advance and keep their dreams of a league and cup double alive.
Wolfsburg fought for the whole 90 minutes, but could not find a way back into the game and left the field to the applause of their fans, who recognised their efforts in reaching the last four.
The attention for both teams will quickly return to the Bundesliga where Stuttgart host Bayern Munich in a decisive fixture for the top three on Saturday while Wolfsburg still need a few more wins to be certain of their top-flight status.
Da Silva provided the only moment of inspiration in a disappointing first half.
His 25-yard free-kick dipped over the wall and into the side of the goal keeper Simon Jentzsch was not guarding.
Wolfsburg reacted and, early in the second half, they thought they were level when Marcelinho beat Timo Hildebrand only for a dubious offside decision to count against the Brazilian striker.
Minutes later, Cacau had the chance to kill off the Wolves when he was put through by Benjamin Lauth, but he could not beat Jentzsch in a one-on-one situation.
As time ran out, Marcelinho attempted to repeat da Silva's free-kick at the other end, but he lifted the ball over the crossbar.