The Bavarians, who head the Bundesliga by 17 points from a distant Dortmund, also have Champions League glory in their sights.
Arjen Robben scored to give Bayern a 1-0 home victory over Dortmund in front of a 71,000-strong crowd - including UEFA president Michel Platini - at the Allianz Arena.
Now the semi-finals await Jupp Heynckes and his impressive team.
Robben made the breakthrough with a curling strike from 20 yards in the 43rd minute, and Bayern clung to their lead as they avenged defeat in the final by Dortmund last year.
Heynckes said on dfb.de: "It was a very intensive match with two high-quality teams, we were that one goal better. We had more chances in the first half. Dortmund were very hard-running, very aggressive.
"With a match on such a level small things can decide it. We were a touch more aggressive today and really wanted this victory."
Stuttgart also reached the last four, beating Bochum 2-0.
Christian Gentner netted an 18th-minute opener for the home side and Vedad Ibisevic ended Bochum hopes with Stuttgart's second goal nine minutes from time.