The Bavarians advanced to the German Cup last four after eliminating holders Dortmund, who had also won back-to-back league titles in 2011 and 2012, with a sparkling performance.
They are now odds-on favourites to claim the domestic cup as well as a first Bundesliga title since 2010 having carved out a 17-point lead over second-placed Dortmund.
Bayern are also enjoying a sensational season in Europe and are all but through to the Champions League quarter-finals after their 3-1 first leg win at Arsenal earlier this month.
"My team deserves a great compliment because it showed that it is not only capable of playing beautiful football at the moment but that it can also fight," coach Jupp Heynckes said.
Bayern's performance so far this season may have pointed towards a win on Wednesday but they have endured a dismal record against their opponents, failing to beat Dortmund in any of their last six encounter and losing five in a row.
With the 'Dortmund curse' finally snapped, Bayern bosses breathed a sigh of relief.
"The issue about supremacy in Germany has now been cleared. I had asked myself how I will survive this game," Bayern president Uli Hoeness confessed.
"But it worked out fine because the team played very well. We have now taken a big step to be back at the very top in Germany."
Hoeness admitted the competition with Dortmund in recent seasons had also helped Bayern improve.
"I have no problem with Dortmund and they are doing superb work," he told reporters. "Borussia lifted us to a new level and we saw the results on Wednesday when we played perfect football at times."
Bayern this season have bounced back remarkably well after a bitter Champions League final defeat last year in Munich and losing out to Dortmund in the German title race.
"We want to win titles," said Robben, who scored the winner and is eager to re-establish himself as an automatic starter after playing mostly as a substitute of late.
"We are strong and stable and the organisation within the team is perfect."
