The visitors began brightly and surged into a two-goal lead within the opening 10 minutes of the encounter.
The first half ended with Bayern narrowly ahead, but Jupp Heynckes's charges delivered another quickfire goal haul after the restart to put them out of reach in the tie.
Muller latched on to Thiago Alcantara's incisive ball over the Leverkusen defence to fire home on 52 minutes and, on the hour, the provider turned scorer by shooting through a crowd of defenders.
Bayern added a fifth moments later, Muller getting the final touch from yet another Ribery delivery, though Leon Bailey grabbed Leverkusen's second via a neat free kick on 72 minutes.
Muller, however, had the final say by sealing his hat-trick on 78 minutes, converting Thiago's free kick with a turn and shot into the right-hand corner of the net for a resounding victory.
Bayern remain on course for the treble, having already sealed the Bundesliga title and preparing to face Real Madrid in the Champions League semi-finals.
BAYER LEVERKUSEN (4-2-3-1): Leno; L. Bender, S. Bender, Tah, Retsos (Bailey 46'); Aranguiz, Baumgartlinger (Alario 61'); Bellarabi (Henrichs 67'), Havertz, Brandt; Volland
BAYERN MUNICH (4-1-2-3): Ulreich; Kimmich, Boateng, Hummels, Alaba (Rafinha 46'); Martinez; Muller (Rodriguez 80'), Alcantara (Sule 85'); Robben, Lewandowski, Ribery