Jurgen Klopp's men are Berlin-bound for a date in the final with either Bayern Munich or Borussia Monchengladbach after a last-gasp goal put an end to the hosts' dream
Ilkay Gundogan saw his powerful effort deflect into the bottom corner in the final minute of extra time, leaving the Cloverleaves crestfallen.
Despite a bright opening few minutes for the hosts, Dortmund soon clamped down and controlled the midfield. But for all their possession, they struggled to create any decent openings.
Robert Lewandowski and Mats Hummels could not convert early half-chances and the best opportunity came with 31 minutes played.
Kevin Grosskreutz headed the ball back across goal for Shinji Kagawa but the Japanese somehow missed the target. With the goal gaping, Kagawa managed to head over the bar from inside the six-yard box.
Furth began the second half in a similar manner to that with which they started the game. They showed great positivity but failed to create a goal scoring opportunity and the momentum soon fizzled out.
With just over 10 minutes played since the restart, BVB had two chances to take the lead in quick succession. Max Grun first made a terrific save from Grosskreutz’s header and then Kagawa screwed an effort just the wrong side of the post from the wide-man’s cutback.
Furth’s first real attempt on goal came with an hour played. Heinrich Schimdtgal centred the ball but Olivier Occean failed to keep his header down and work Roman Weidenfeller.
Dortmund were struggling to get a hold of the game and in the 73rd minute they spurned another great chance. Some sloppy defending from Furth enabled Grosskreutz to penetrate the area and shoot. He failed to capitalise as his attempt sailed narrowly over the bar.
The hosts only threatened sporadically but in the 78th minute Occean once again failed to get his header on target, allowing Dortmund a narrow escape.
With neither team capable of finding the back of the net in the standard 90 minutes, the game went to extra time.
The Cloverleaves were unfazed and did not sit back and hope for the best against the misfiring Bundesliga leaders. Occean came agonisingly close to nodding in from Schimdtgal’s free kick in in the 96th minute.
One could not tell that Dortmund played in a higher league than their hosts and with the extra time interval looming, Weidenfeller was forced into a save from Schmidtgal with a well-struck free kick.
In the final moments of the additional 30 minutes, Furth coach Michael Buskens opted to bring on a substitute goalkeeper in Jasmin Fejzic but the game was to be decided before the shootout.
In the final minute, substitute Gundogan saw his effort bounce off the post and go into the net via the substitute goalkeeper's back in the final minute of extra time.
The win keeps Jurgen Klopp’s hopes of a domestic double alive and his team will face either Bayern Munich or Borussia Monchengladbach in the final. Furth meanwhile will turn their attentions back to the league as they aim to achieve promotion from the 2. Bundesilga.
It is good news for other Bundesliga teams as the Europa League qualification spot awarded to the winner may well be transferred to the league providing BVB, Bayern and Gladbach all finish in the top seven.