With Borussia Dortmund dropping more points earlier in the day, the Bavarians had the chance to extend their lead at the summit but they did not get the start they had wished for.
However, Christopher Nkunku opened the scoring for the visitors on 19 minutes with a composed finish beyond Manuel Neuer, after latching onto Emil Forsberg's through ball.
Jamal Musiala, who replaced the injured Javi Martinez, equalised for Bayern on 27 minutes after turning home a cross from the lively Kingsley Coman.
Coman was at his best once again 10 minutes before the break as his inviting cross found Thomas Muller in the box, and the German attacker made no mistake from close range.
Leipzig had the final say in the first half though as Dutch winger Justin Kluivert collected a pass from Amadou Haidara before firing past Neuer to send the sides in to the break all square.
It didn't take Leipzig long to regain the lead in the second half when Forsberg fired first home from close range three minutes after the halftime break.
When it looked as if Leipzig could get a fourth goal, Muller brought Bayern level with 15 minutes left on the clock after headed home Koman's cross.
Hans Flick's men were unabe to find a winning goal late on, but 3-3 was how the encounter clash ended in Munich.