In its maiden league match since the departure of head coach Niko Kovac, the German champion made relatively light work of its opponent in the first top-flight Klassiker of the season to bounce back from a 5-1 thrashing by Eintracht Frankfurt last week.
Lewandowski struck twice against his former club, with Serge Gnabry also on the scoresheet before a Mats Hummels own goal condemned Dortmund to a sixth consecutive Bundesliga defeat at Allianz Arena.
While the result will help caretaker boss Hansi Flick's hopes of staying in charge of Bayern until at least the end of the season, Lucien Favre's position at Dortmund is now beginning to look shaky.
Dortmund knows only too well the danger of Lewandowski, but it granted the Poland striker the freedom of the penalty area to head home the opening goal from Benjamin Pavard's cross from the right.
Bayern was comfortable in the first half, with Axel Witsel firing over in the 45th minute when Dortmund at last managed a shot, the visitors having taken off Jadon Sancho nine minutes earlier.
Bayern took full control of proceedings two minutes after the restart, Thomas Muller racing clear down the left and crossing for Gnabry to finish after Lewandowski failed to make contact with the ball.
Lewandowski should have made it 3-0 just before the hour mark, collecting Kingsley Coman's pass, turning on to his right foot and curling a shot just past Roman Burki's left-hand post.
Substitute Paco Alcacer went close to halving the deficit before Muller took his assist tally in the Bundesliga to 101 since the 2004-2005 season, gathering Lewandowski's pass and chipping the ball back to his strike partner, who tucked the ball beneath Burki.
With Dortmund's resistance broken, Hummels turned into his own net when under pressure from Thiago Alcantara to compound a miserable outing against his former employer.
Bayern is now back to within a point of league leader Borussia Monchengladbach, having played a game more, and will likely still consider itself a title favourite regardless of who becomes its permanent new head coach.
As for Dortmund, Favre may now start to feel the pressure. His side has won only three of its past nine league games and could be six points off top if Gladbach beats Werder Bremen on Monday (AEDT).