Rampant Bayern equalled their record of eight consecutive wins at the start of a season.
Germany forward Mueller opened his account in the 26th minute, latching onto a 50-metre ball from defender Jerome Boateng and he doubled the hosts' lead with a penalty nine minutes later for his eighth league goal.
Pierre-Emerick Aubameyang kept up his remarkable run of scoring in every one of Dortmund's league matches this season as he slotted in from close range a minute later but his team could not stop the charging Bavarians, who had 15 shots on goal in the game.
Irrepressible Bayern forward Lewandowski killed off any hopes of a comeback with two goals early in the second half to take his tally to 12 goals in all competitions in the last 12 days alone and nine in the last three Bundesliga matches, a league record.
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Boateng floated over another cross from his own half and Poland captain Lewandowski shook off both Mats Hummels and Sven Bender to score a minute after the restart.
He then slotted in 12 minutes later for his 12th league goal in the first eight matchdays, equalling the Bundesliga record set by Christian Mueller in 1964/65 and Gerd Mueller in 1968/69.
Former Dortmund team mate Mario Goetze added a fifth goal for dazzling Bayern in the 66th with the visitors having surrendered.
"I want to congratulate my players," said modest Bayern coach Pep Guardiola. "We had some problems in the opening 15 minutes and until the goal we did not have many chances."
Bayern, who are chasing a record fourth consecutive league crown, are on 24 points, seven clear of Dortmund.
"We had a good start, defended well," said Dortmund coach Thomas Tuchel. "But we had imagined it differently. We must accept that we were not good enough on the day."
Schalke 04 missed the chance to move into second place following a 3-0 defeat by visitors Cologne, a result that ended their four-game winning streak in the Bundesliga and left them in third, a point behind Dortmund.
Champions League club Bayer Leverkusen squandered a penalty through Hakan Calhanoglu to draw 1-1 against lowly Augsburg and drop to seventh place on 13.
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
