Reigning champion Bayern dominated from the start in its Allianz Arena stadium with Polish international Lewandowski grabbing a double as he was on the scoresheet for the 11th straight league match.
The emphatic victory has lifted Bayern up to third in the standings, one point adrift of leader Borussia Moenchengladbach, which can extend the advantage at home to Werder Bremen Sunday.
Dortmund has slipped to fifth, three points adrift after a disappointing afternoon for Lucien Favre’s men.
It was the second straight win for interim Bayern coach Hansi Flick, who will stay in charge for the next match against Fortuna Dusseldorf on November 23, the club has confirmed after reports that former Arsenal manager Arsene Wenger had been approached over the vacant job.
Bayern chairman Karl-Heinz Rummenigge told Sport 1: “We will work with Hansi Flick until further notice. I have respect for Arsene. We will call him and clear things up. I don’t want to stress him.”
Making light of the off-field troubles, Bayern was quickly off the mark in the classic fixture, with Lewandowski powering home a superb header from a Benjamin Pavard cross on 17 minutes.
Dortmund star winger Jadon Sancho was substituted as early as the 36th minute as he failed to make an impact and shortly after the break Serge Gnabry fired home the second after Lewandowski had failed to convert from close range.
Lewandowski made no mistake later in the half, his 23rd of the season having scored in all of Bayern’s fixtures in the league and Champions League this campaign.
A Mats Hummels own goal completed a miserable afternoon for Dortmund.
“We were very focused, we knew we had to give 100 percent and improve,” said Lewandowski after the match.
30th anniversary marked
Earlier, RB Leipzig went to second in the Bundesliga, heading Bayern on goal difference with a 4-2 win at Hertha Berlin in the Olympic stadium.
Before the match, to mark the 30th anniversary of the fall of the Berlin Wall, players stood on either side of a replica wall which had been built to mark the historic events of November 9th, 1989.
The wall was symbolically knocked down prior to the start of the match which saw a fine start for the host as midfielder Maximilian Mittelstaedt scored the opener in the first half.
However, Timo Werner equalized from the penalty spot for the visitor and Marcel Sabitzer added Leipzig’s second on the stroke of the halftime break.
Leipzig midfielder Kevin Kampl put his side 3-1 ahead with a superb strike before Werner grabbed his second for his 11th league goal in as many games.
Hertha striker Davie Selke grabbed a late second for his side against his former club.