Led by new captain Philipp Lahm after Dutchman Mark van Bommel joined AC Milan on Tuesday, Bayern took the lead after 25 minutes with Mario Gomez tapping in a Luiz Gustavo low cross.
Aachen had a brief good spell in the second half but Thomas Muller sealed Bayern's ticket when he fired in through the legs of keeper David Hohs in the 75th minute.
The Germany international added another with a low drive from 14 metres four minutes later and Arjen Robben, who came on as a substitute, completed the rout in the 88th minute.
The win is expected to take some pressure off Bayern coach Louis van Gaal, at odds with club bosses over some of his decisions, including the release of captain van Bommel after four and a half years.
A goal from Chinese Shao Jiayi six minutes from time sent second division Energie Cottbus through with a 1-0 win over Hoffenheim with their new signing Ryan Babel from Liverpool in the starting line-up.
Duisburg threw out another Bundesliga team when they beat Kaiserslautern 2-0.
On Tuesday Schalke 04 needed a last minute goal in extra time from 17-year-old Julian Draxler to advance 3-2 past Nuremberg.
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