Substitute Michael Olise was the star of the show, providing a hat-trick of assists as the Bavarians scored five unanswered goals in the second half to claim the emphatic victory.
Fourth-placed Leipzig were looking good to hand Bayern their first defeat of the Bundesliga season after a strong first-half showing in which Romulo Cruz gave them the lead in the 20th minute.
However, it was a completely different story after the break as Bayern Munich came out all guns blazing and took the game away from the hosts.
Serge Gnabry grabbed an equaliser just five minutes after the break in a sign of things to come.
Olise was introduced in the 56th minute and completely changed the game as he provided assists for Harry Kane (67'), Jonathan Tah (82') and Aleksander Pavlovic (85') before scoring himself in the 88th minute to add the cherry on the cake.
The win takes Bayern Munich to 50 points, 11 ahead of closest rival Borussia Dortmund and in an increasingly commanding position to claim the league title this season.
Elsewhere in the Bundesliga over the weekend, Wouter Burger's ninth-minute strike was enough to hand Hoffenheim a 1-0 win over Bayer Leverkusen at PreZero Arena, while HSV and Borussia Monchengladbach drew 0-0 at Volksparkstadion.
Goals from Adrian Beck (45+1') and Moritz Jenz (80') cancelled each other out as Wolfsburg and Heidenheim drew 0-0 at the Volkswagen Arena and a brace from Ragnar Ache (57', 85') was enough to hand FC Koln a 2-1 win over Mainz at RheinEnergieStadion, with Stefan Bell scoring for the visitors in the 29th minute.
Dortmund needed a late Emre Can penalty to prevail 3-2 over St Pauli in a thrilling encounter at Signal Iduna Park.
Julian Brand opened the scoring on the stroke of half-time for the hosts, with Karim Adeyemi doubling their advantage in the 54th minute.
St Pauli fought back well, though, with goals from James Sands (62') and Ricky-Jade Jones (72') pulling them level before Can sunk a penalty five minutes into stoppage time to hand Dortmund a dramatic late victory.
On Friday night, a back-and-forth clash between Werder Bremen and Eintracht Frankfurt ended in an epic 3-3 draw at Weserstadion.
Arnaud Kalimuendo got the visitors on the scoresheet inside the opening minute before Justin Njinmah levelled for the hosts in the 20th minute.
Nnamdi Collins restored Frankfurt's lead in the 56th minute, with Jens Stage getting Bremen back on level terms once again in the 78th minute.
Within 120 seconds of Stage's strike, Jovan Milosevic put the home side ahead for the first time in the game in the 80th minute but Ansgar Knauff ensured the spoils would be shared with a late equaliser four minutes into stoppage time at the end of the match.