Holders RB Leipzig kept their hopes of a second straight German Cup title alive, winning 2-0 against Borussia Dortmund to reach the semi-finals on Wednesday.

The home side started fast against a poor Dortmund, taking the lead midway through the first half when a rampaging Mohamed Simakan found Timo Werner on the break to tap home from close range.

Defender Willi Orban scored on the counter deep into injury time to send Leipzig through to the semis for the fourth time in five seasons.

After the game, Orban toasted "a beautiful ending for us" after an "emotional match, from both sides."

Dortmund captain Marco Reus told German TV "in the first half, Leipzig ate us up".

"We did not deserve to win that game," he added.

Dortmund midfielder Julian Brandt said his side were "extremely lucky to have survived the opening stages only conceding one goal."

The two most recent Cup winners faced off in what has become an increasingly bitter rivalry between the sides most likely to challenge Bayern Munich for major trophies in Germany.

With Bayern eliminated by Freiburg on Tuesday, both sides knew a win would place them in pole position for the Cup.

Leipzig came into the match having lost four of their past five matches but showed fluency and aggression in attack, peppering a shellshocked Dortmund defence.

Visiting goalkeeper Gregor Kobel, after a howler which led to his side's collapse on Saturday against Bayern, held firm, pulling off several acrobatic saves in the early stages.

Leipzig eventually claimed a deserved lead on 22 minutes, Simakan running 50 metres to set up Werner for the former Chelsea striker's fifth goal this Cup campaign.

Despite a raft of attacking changes from coach Edin Terzic, Dortmund were ineffective up front, missing the link-up play of injured striker Sebastien Haller.

Dortmund dominated possession late on and went close to scoring deep into injury time, but with Kobel pushed up, Leipzig scored a second through Orban on the break to seal the victory.

Dortmund, who opened 2023 with 10 straight wins in all competitions, have now lost three of their past five.

Sitting two points behind Bayern in the league, Dortmund will need to arrest the slide at home against third-placed Union Berlin on Saturday.

Earlier on Wednesday, Enzo Millot scored late to send Stuttgart into the last four with a 1-0 win at Nuremberg.

With the match heading towards extra time, Millot latched onto a Hiroki Ito pass and chipped home goalkeeper Peter Vindahl, giving Stuttgart coach Sebastian Hoeness a win 48 hours after he replaced the sacked Bruno Labbadia.

Kick-off was put back by half an hour due to delays caused by fans entering the sold-out stadium.

The only second-division side in the last eight, Nuremberg were trying to salvage some pride after a poor league season which has left them fighting to avoid relegation.

Stuttgart are bottom of the Bundesliga and both teams played out a dour first half.

Early in the second period, Stuttgart defender Waldemar Anton almost gave the visitors the lead, but his header was saved by Vindahl.

With less than 10 minutes remaining, Millot broke the deadlock.

Stuttgart withstood a last wave of Nuremberg attacks to keep their quest for a fourth German cup alive.

Stuttgart and Leipzig joined Freiburg and Eintracht Frankfurt in the semis.