Robben, Mueller strike as Bayern win German Cup
Bayern Munich's midfielder Arjen Robben celebrates scoring during the extra-time of the German Cup final at the Olympic Stadium in Berlin on May 17, 2014 - by Odd Andersen
After the first 90 minutes finished goalless, Robben broke the drought in the 107th-minute before Mueller added a second in time added-on.
Coach Pep Guardiola finishes his first season in charge of Bayern with four trophies having already won the Bundesliga title, Club World Cup and UEFA Super Cup.
Bayern won the German Cup for a record 17th time to claim the domestic league and cup double -- the Champions League was the only title to evade the Bavarian giants this season.
Having also scored the late winner in the 2013 Champions League final against Dortmund at Wembley, Netherlands winger Robben again broke Dortmund hearts.
And there was no fairytale finish for Poland striker Robert Lewandowski who had promised to finish his four years at Dortmund by lifting the cup before joining Bayern next season.
This was the fourth and final time Germany's top two sides met this season with both sides finishing with two wins a piece.
But it was a nervy, tense affair in front of a 71,967 crowd at Berlin's sold-out Olympic Stadium which also included Hollywood star Tom Hanks who is filming 'A Hologram for the King' in Germany's capital.
Bayern were forced into a late change when Austria left-back David Alaba dropped out with a stomach muscle injury and Brazil's Rafinha slotted into his place.
Munich were already without defensive midfielder Bastian Schweinsteiger, ruled out with a knee injury while striker Mario Mandzukic having been dropped.
Guardiola opted to play a new 3-4-3 system and included 18-year-old midfielder Pierre-Emile Hoejbjerg, who was making only his 11th first team appearance.
Dortmund were at near full strength with Lewandowski making his final appearance in the yellow-black shirt.
Bayern made a bright start as Mueller and Robben both forced Dortmund captain and goalkeeper Roman Weidenfeller into early saves.
- Lahm leg injury -
There were worrying scenes ahead of next month's World Cup in Brazil when Bayern's Germany captain Philipp Lahm limped off with half an hour gone to be replaced by Franck Ribery.
The Bayern bench said Lahm had taken a knock to the fibula, but it was not serious and he is expected to join the Germany training camp which starts on Wednesday.
Hoejbjerg squandered a great chance with half-time approaching when he fired wide from the penalty area after being left unmarked.
At the other end, Lewandowski cannoned his shot over the bar moments later.
Both teams had clear chances in the second half as Mueller's shot at point-blank range was smothered by Weidenfeller on 56 minutes.
And at the other end, Dortmund defender Mats Hummels' header was saved off the line on 64 minutes by Bayern's Dante.
After the game went to extra-time, Robben broke the drought when he fired home at the near post from five metres out.
Mueller then took advantage of tired Dortmund legs when he held off Germany team-mate Marcel Schmelzer and rounded Weidenfeller just before the final whistle as Bayern defended their cup title.