The Bundesliga giants handed Barcelona a brutal demonstration of how far their opponents have fallen as Mueller scored the opening goal at the Camp Nou before Robert Lewandowski netted twice.
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 visitors only had themselves to blame as Thomas Mueller missed a clear late chance, nine minutes from the end, when he fired wide with the goal at his mercy and England 1-0 up.
Late goals by Raheem Sterling and Harry Kane at Wembley put England into the quarter-finals Tuesday and brought down the curtain on Loew's 15-year reign as Germany coach.
Hernandez has spent two seasons with Bundesliga champions Bayern since his 80 million euros ($97 million) transfer from Atletico Madrid in 2019.
Four years after Mueller contributed five goals as Germany triumphed over Argentina in Brazil, Loew said the misfiring Bayern star was keen to make amends.
The draw in front of a sold-out 50,653 crowd preserves both sides' respective unbeaten runs dating back to Euro 2016.
Robert Lewandowski, the Bundesliga's top scorer, converted a late penalty to claim his 14th goal in as many games for Bayern this season.
Thomas Mueller put the hosts ahead after 17 minutes before goals by Joshua Kimmich and Mats Hummels sealed the victory.
Explaining the team's poor start by their standards, Mueller said there are things that have not been 100 percent successful.