German Super Cup: Robert Lewandowski, Thomas Mueller on target as Bayern Munich beat Borussia Dortmund
New coach Julian Nagelsmann has earned a trophy, which Bayern also won last year against Dortmund in Munich, with his first win in charge.
The 21-year-old set up three goals and scored two after starting the season with a hat trick in the German Cup last weekend.
Champions League: Marco Reus, Mats Hummels injury doubts for Borussia Dortmund against Manchester City
Dortmund is in fifth place in the Bundesliga and would miss out on Champions League qualification for next season unless it can win this season's competition.
The Germans needed to win by two clear goals in their final group F match at Kazan stadium to advance to the last 16.
Joachim Loew's team need to win by a two-goal margin in Kazan to be sure of advancing to the knockout rounds.
There was near silence from the half-full south stand, which normally holds 24,500, as the club backed the supporters' silent protest.
Dortmund travel to the Santiago Bernabeu for a dead rubber Champions League tie with holders Real already qualified for the last 16 while the Germans cannot advance.
Germany winger Marco Reus claimed a hat-trick on his comeback as Borussia Dortmund hammered Legia Warsaw 8-4.