It’s been six years since Bayern last won this trophy - their longest drought since a 12-year run that ended in 1998 - and it initially looked as though their wait may continue.
A sensational mazy run from Yan Diomande ended with the Ivorian playing in Christoph Baumgartner, who fired into the far corner, but the 26-year-old had his celebrations cut short when a VAR review ruled him offside.
That prompted a strong response from the hosts, with Harry Kane having an effort cleared off the line by Castello Lukeba before the England captain volleyed wide from Michael Olise’s cross.
An entertaining - but ultimately goalless - first half came to a close with both goalkeepers being called into sharp saves from shots by David Raum and Aleksandar Pavlovic.
Making that second stop was Maarten Vandevoordt, who produced another to keep out Serge Gnabry after half-time, but the Belgian went from hero to zero just after the hour mark when he took down an onrushing Josip Stanisic in the area.
Kane stepped up and placed the subsequent penalty into the bottom corner, finally adding a goal to an all-action performance.
Bayern had no intention of letting up after that, scoring again just a few minutes later when Luis Diaz escaped the defence and ran onto Olise’s ball before slotting under the goalkeeper.
Leipzig attempted to find a way back into the tie but were ultimately kept at arm’s length by Der Rekordmeister, who are now unbeaten in seven meetings.
More importantly, though, their treble dream remains intact. Meanwhile, Leipzig’s performance was a lot more encouraging than their 6-0 and 5-1 defeats to these opponents earlier in the season, but they will have to wait at least another year for a chance to add to their 2022 and 2023 titles.
Flashscore Man of the Match: Michael Olise (Bayern)