Both sides went into the match level on points in first and second, but a dominant first-half display from the champions saw them dispatch of their newest challengers and move three points clear.
In a match billed as the kings of German football against the young upstarts, Leipzig made the brighter start to the contest as they looked to bring a perfect end to a dream first half of the season.
The unlikely title challengers, who are in just their eighth year of existence and their first season in the Bundesliga, came close to stunning the football world once again within four minutes when the lively Timo Werner drilled a low ball across the face of goal that Yussuf Poulsen was inches away from turning in.
Bayern soon began to flex their muscles and take control of the contest, though, and they were almost gifted an opening goal when former Liverpool goalkeeper Peter Gulacsi spilled Douglas Costa's cross into a dangerous area, but Marcel Halstenberg was there to clear the danger before Arjen Robben or Robert Lewandowski could turn it home.
The hosts did break the deadlock just three minutes later, though, as Robben and Philipp Lahm combined down the right to play a low ball in towards Lewandowski. The Pole's effort crashed against the post, but Thiago Alcantara was following in to bundle home the rebound.
It was almost two goals in as many minutes for Carlo Ancelotti's side when they once again played through the Leipzig defence, but Costa's powerful drive from the left side of the area hit the outside of the near post on its way behind.
A loose pass from Naby Keita under pressure from Arturo Vidal gifted possession to Lewandowski, who combined with Thiago to slip the ball through for an overlapping Xabi Alonso. The midfielder proceeded to place his finish into the bottom corner for his first ever Bayern goal from inside the penalty area.
The second goal left Leipzig with a mountain to climb, but they almost responded within four minutes when Willi Orban was left unmarked from a corner, only to see his firm header kept out by a smart stop from Neuer.
Any slim hopes the visitors had of writing another memorable chapter into their record-breaking season were well and truly extinguished on the half-hour mark, though, as Emil Forsberg was shown a straight red card for a poor challenge from behind on Lahm, leaving Leipzig to play an hour with just 10 men.
Bayern's dominance only increased with their numerical advantage, and a third goal arrived right on the stroke of half time when Lewandowski sent Gulacsi the wrong way from the penalty spot after the keeper had brought down Costa inside the area.
The goal saw Lewandowski draw level with Giovane Elber as the second-highest scoring foreign player in Bundesliga history, and also saw him become the only active player to have scored against all 18 of the current Bundesliga teams.
The Pole should have had another seven minutes into the second half when he latched on to a clever reverse pass from Costa, but Gulacsi stood up well to deny the striker in a one-on-one situation.
Lewandowski had another one-on-one chance shortly after the hour mark when he played a one-two with Franck Ribery on his way into the box, but once again he was unable to find a way past the keeper having this time gone for the chip.
Thiago, Juan Bernat, Ribery and Costa all threatened with sights of goal in the final 20 minutes as Gulacsi was kept busy, but Leipzig continued to hold out in damage limitation mode.
It was in the final five minutes that the hosts really lay siege to the Leipzig goal, though, and they were inches away from a fourth when Ribery worked space for a shot before firing a powerful effort off the underside of the bar which bounced down onto the line and out.
Ultimately Bayern were forced to settle for a three-goal victory, which extends their winning streak to six matches in all competitions, including four consecutive clean sheets.
Ancelotti's side are now not in action again until January 20, when they resume the Bundesliga season against Freiburg.