The home team took the lead inside 30 seconds when Michael Olise set up Jamal Musiala, who tapped in from close range. Just over a minute later, however, the visitors equalised when Benjamin Sesko stroked home Lois Openda's dangerous cross.
Konrad Laimer scored against his old side in fine fashion when he volleyed in Olise's pinpoint delivery in the 25th minute, before Joshua Kimmich's 25-yard piledriver 11 minutes later put Bayern in control.
The returning Harry Kane endured a frustrating night, punctuated by moments of real quality and rustiness you would expect from someone who has been out injured for several weeks. The wheels well and truly came off of Leipzig's wagon when Leroy Sane and Alphonso Davies scored two quick-fire goals in the final quarter of the game.
The result ensured Bayern bounced back in ideal fashion from their shock 2-1 loss to Mainz last weekend as they went seven points clear at the top of the Bundesliga on Friday night.