Erling Haaland scored twice in the opening nine minutes but Robert Lewandowski showed he is still the finest striker in Germany with a stunning hat-trick in Der Klassiker.
Haaland gave Borussia Dortmund the lead at the Allianz Arena after just 80 seconds with a deflected strike from the edge of the area.
The Norwegian doubled the visitors' advantage seven minutes later, finishing from Thorgan Hazard's cross after a sweeping team move.
But Lewandowski was on hand to thwart his former club and pulled Bayern back on level terms by the half-time whistle.
The prolific Pole poked in from Leroy Sane's cut-back in the 26th minute before slotting a penalty into the bottom corner after Kingsley Coman was felled by Mahmoud Dahoud in the area.
Der Klassiker continued at a frantic pace after the interval with Serge Gnabry threatening and Niklas Sule going closest for the hosts, and Dortmund ace Marco Reus causing the Bayern backline problems.
Bayern had the lion's share of possession and shots – and made their dominance count in the 88th minute as Leon Goretzka fired the Bavarians in front on the half-volley.
And Lewandowski sealed a famous comeback victory with his third of the night, rifling in from the edge of the box after splendid work by Alphonso Davies on the left flank.
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The result sees Bayern maintain their two-point advantage at the top of the Bundesliga after the gap was momentarily closed by RB Leipzig, who won 3-0 at Freiburg earlier on Saturday.
Dortmund, on the other hand, sit sixth in the table as their turbulent season continues.
Meanwhile, Lewandowski's hat-trick takes his tally for the season to 37 goals in 30 appearances in all competitions, and 31 goals in 23 Bundesliga games.
He is averaging 1.43 goals per 90 minutes in the league and is on course to shatter Gerd Muller's record of 40 goals in a single Bundesliga campaign, which the Germany legend set in the 1971/92 season.
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At 32 years of age, Lewandowski remains the most prolific forward in Germany and arguably the finest striker in Europe.
His nearest rival in the Bundesliga scoring charts is Haaland, who has 19 goals in 19 Bundesliga games and 27 goals in 24 appearances in all competitions.
The 20-year-old remains one of the hottest prospects on the continent, but Lewandowski is not ready to pass the baton to the next generation just yet.
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