This represented an important match for Bayern, not only because a win would take them closer to ending their drought in the Pokal, but also to keep their treble hopes alive.
It was a strong start from Vincent Kompany’s men, who went close with a curling effort from Luis Díaz which was turned wide by Mark Flekken.
Leverkusen had some brief joy with their own attacking play thereafter, but the visitors were back well on top by the 20th minute, and were soon celebrating the opener.
Michael Olise’s flick on the right side released Jamal Musiala, who elected to pull it back into the area for Harry Kane to steady himself and bury it into the roof of the net.
In search of a second, Bayern remained on top and had both Joshua Kimmich and Olise test Flekken, before Kane nearly made it 53 competitive goals for the season by hitting just over with a powerful volley.
The half ended with things threatening to boil over, and the sides used that passion to continue to push at both ends after the restart.
Robert Andrich retreated to boot Díaz’s chipped finish off the line, but his heroics were soon matched by Manuel Neuer, who pulled off a fantastic stop of Nathan Tella’s drive from the edge of the area.
Feeling that one goal might not be enough against a side who had scored at least three times in each of their previous six Pokal home games, Bayern pushed for more, and Flekken ensured Kane didn’t complete what would have been a 16th brace of the season.
Leverkusen’s own fortunes took an upturn with about 20 minutes to go though, with Patrik Schick meeting Jarell Quansah’s cross and heading just over, but they failed to create much from there.
Instead, Bayern hit them on the counter in the final seconds, as Leon Goretzka sent Díaz through to delicately chip into the net.
With the league title already sealed, Germany’s most successful club by all metrics can now turn their attention to the Pokal final – where they will face either Stuttgart or Freiburg – as well as a UEFA Champions League last-four date with holders Paris Saint-Germain.
Leverkusen, meanwhile, have drawn a blank since their domestic double two years ago, and fans will hope their wait for another trophy isn’t as long as their previous 31-year drought.
Flashscore Man of the Match: Michael Olise (Bayern Munich)