Edin Terzic’s side, who were without Jadon Sancho and Raphael Guerreiro, did not appear to miss them as they scored twice in the opening nine minutes through Erling Halaand.
Haaland got his first with a deflected strike from outside the box before making it 2-0 with a tap in from Thorgan Hazard’s pass.
Leipzig take over lead in Bundesliga with win at Freiburg
The visitors then went into ultra defensive mode and invited the Bavarians onto them with disastrous consequences.
Lewandowski pulled a goal back with a close range finish and then netted the equaliser with a penalty to cap off a pulsating first-half.
Hansi Flick’s side dominated the second period but were dealt an injury blow with Jerome Boateng limping off with a suspected hamstring injury.
In the final two minutes, Leon Goretzka netted with a volley before Lewandowski completed his hat-trick with a brilliant strike for his 31st goal in 28 games.
The result sees Bayern go top of the table while Dortmund remain in sixth place.
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