Leipzig thought they had scored the opener within the first five minutes, as Yan Diomande cut in from the right, jinked his way past three challenges, and found Christoph Baumgartner, who finished smoothly. A VAR check, though, revealed that Baumgartner was offside.
Before the 20-minute mark, Harry Kane had his first major opportunity to hit the back of the net, seeing his effort from 12 yards cleared off the line. Kane then saw a back-post header blocked by his own team-mate Aleksandar Pavlovic, albeit inadvertently, before Luis Diaz slammed an effort over the bar.
Baumgartner nearly opened Bayern up before half-time, as he found David Raum, but his powerful effort was well-saved by Manuel Neuer.
Before half-time, Marten Vandervoort made two exceptional saves to keep Leipzig level, but in the second half, just after the hour mark, his dangling leg brought down Josip Stanisic, and Kane stepped up to finally hit the back of the net from 12 yards.
And within three minutes, Bayern had their second, thanks to a vicious finish from Diaz after a brilliant pass from Michael Olise.
Now, the Bavarian giants have a semi-final to prepare for - the first time they have reached this stage in this competition since 2020.
