RB Leipzig was harshly reduced to 10 men when Naby Keita was sent off, and Sven Ulreich made a clutch save in the shootout to send Bayern through.
In a preview to the Bundesliga clash between these two sides on Saturday, RB Leipzig were cruelly knocked out of the DFB Cup, via a penalty shootout, to keep Bayern Munich's hopes of securing a domestic double alive.
There was a frantic opening 20 minutes of the match, with both sides showing their attacking threat. Robert Lewandowski carved Bayern's first opportunity of the game, while Jean-Kévin Augustin and Emil Forsberg were proving to be the danger men for die Roten Bullen.
Just after the half hour mark, Arturo Vidal carelessly fouled Yussuf Poulsen on the edge of the area and the referee pointed to the penalty spot.
However, protests from the Bayern Munich players made the ref consult his fifth official and without the assistance of VAR, the original decision was overturned and Leipzig had to settle with a free-kick.
Bayern went into the half-time break as the weaker team, however, French winger Kingsley Coman was the first man to create a chance just one minute after the restart.
Leipzig saw a second penalty shout go against them in the early stages of the second half, Jean-Kévin Augustin the man who went down under a strong challenge from Jérôme Boateng.
RB Leipzig were a man down just 10 minutes into the second half after Naby Keita, who picked up his customary yellow card in the first-half, was given his marching orders after naively tugging on the shorts of Lewandowski to stop a Bayern Munich counter attack.
Bayern were in the ascendancy following Keita's red card and their Polish striker should have given the Bavarians the lead just after the hour mark.
However, Lewandowski's low effort flew narrowly past Péter Gulácsi's far post and the former Borussia Dortmund star would soon be regretting that missed opportunity.
Forsberg's goal opened up the game and, having given away a penalty just five minutes earlier, Boateng sent an inviting cross into the box that Thiago Alcântara met with a powerful header to draw Bayern back on level terms.
The introduction of star striker Timo Werner gave Bayern's defence something different to think about in the latter stages of the match, however, the German wonderkid was unable to put his mark on the game and the two sides were forced to play an extra 30 minutes of football.
Péter Gulácsi was forced into an outstanding double save to deny Thiago and Joshua Kimmich in the first half of extra time, while 23-year-old Kwasi Okyere Wriedt and Lewandowski saw their efforts denied by the crossbar.
Leipzig continued to face a barrage of Bayern Munich attacks in the second-half of extra time and despite Timo Werner seeing a goal ruled out for offside, the game finished 1-1 and progression to the next round of the DFB Cup was set to be decided with a penalty shootout.
Bayern were tasked with taking the first penalty and after failing to find a way past Gulácsi in 120 minutes, Robert Lewandowski made it one out of one for the visitors.
Bernardo, David Alaba, Kevin Kampl, Mats Hummels and Marcel Halstenberg all scored their penalties, with Sebastian Rudy also finding the back of the net. Willi Orban scuffed his effort beyond Ulreich and under pressure, Arjen Robben's finish left Werner needing to find the back of the net.
However, the youngster was unable to beat his former VfB Stuttgart teammate and Bayern Munich booked their place in the next round of the DFB Cup.