Although Robert Lewandowski pulled one back in the 75th minute - he scored a hattrick in the German Cup final win over Bayern which completed the double for Dortmund - but the champions were unable to turn things around as Bayern earned a psychological boost ahead of the new season.
The win at the Allianz Arena stadium in Munich also gave veteran coach Jupp Heynckes a trophy to put on his shelf after last season saw the Bavarians fail to win anything.
As well as ceding domestic dominance to Dortmund, Bayern also lost the Champions League final at their home stadium to Chelsea.
On Sunday, they at least put an end to a run of five straight defeats to Dortmund.
Croatian international and €13 million summer recruit Mandzukic bagged the opener with a neat finish from a Frank Ribery cross on six minutes and in the 11th minute Müller was on hand when, after linking with Mandzukic, he fired in when an Arjen Robben effort came back off the post.
Lewandowski then drew a fine save from Manuel Neuer just after the restart before missing a sitter from close range as Jürgen Klopp's champions tried to spark a revival.
The Polish striker then did reduce the arrears before time ran out on Dortmund.