Ten-man Borussia Dortmund have reached the final of the DFB-Pokal after taking Bayern Munich to penalties following a 1-1 draw after extra time and subsequently vanquishing their rivals 2-0 from the spot.

Both sides began the game with plenty of intent but despite a few forays into the opposing final thirds, there was little in the way of concrete chances early.

Thomas Muller came close just before the quarter-hour mark when he flashed a header wide of Mitchell Langerak's post from Xabi Alonso's corner.

Bayern applied more and more pressure as the game went on and duly broke the deadlock on the half-hour mark, Lewandowski charging towards goal on the counter and chipping over the keeper.

The Polish striker was denied by the post but he collected the rebound before slotting home from an incredibly tight angle.

Dortmund had few ideas with regards to countering the Bayern barrage and could have found themselves two down on the stroke of half time, but Lewandowski's audacious 30-yard effort with Langerak off his line flew wide.

The hosts picked up from where they left off after the restart as Mitchell Weiser's pinpoint pass to Muller was thwarted by Langerak in the 47th minute and Lewandowski smashed a shot against the post just before the hour.

Dortmund didn't register their first shot on target until the 72nd minute when Pierre-Emerick Aubameyang's deflected header was comfortably saved by Manuel Neuer.

Much to the surprise of the home crowd Jurgen Klopp's charges then went on to grab the equaliser with just their second attempt as the Gabonese striker bundled Henrikh Mkhitaryan's cutback across the line despite Neuer's last-ditch grasp.

The shellshocked hosts, having dominated for 75 minutes, were forced to hang on for dear life thereafter as Marco Reus and Mkhitaryan came close to bagging a winner for Dortmund, but managed to take the game to extra time.

There was little action in the opening stages with both sides eager to conserve their energy, though Bastian Schweinsteiger came close when Alonso's cross was headed just over by the Germany international from yards out.

Dortmund then suffered a setback in the 108th minute when substitute Kevin Kampl was shown a second yellow card for a pull on Schweinsteiger.

Bayern sensed an opportunity to profit from their man advantage and pushed forward in a bid to snatch a late winner, but despite another missed Schweinsteiger header and a penalty claim when Lewandowski was fouled by Langerak in the box, the game would go on to penalties.

Phillip Lahm opened proceedings from the spot, but he skied his effort over before Ilkay Gundogan smashed his reply into the top corner.

Xabi Alonso was next for Pep Guardiola's charges but he too made a hash of his penalty, blasting wide as Dortmund subsequently doubled their lead through Sebastian Kehl.

That would prove to be the last successful effort from the spot from either side as the visitors hung on to reach the DFB-Pokal final and crush their rivals' bid to clinch the treble of league, cup and Champions League.

Arminia Bielefeld and Wolfsburg contest the second semi-final on Wednesday for the right to take on Dortmund in Berlin on May 30.