Having missed out on UEFA Champions League qualification, Leverkusen was aiming to cause an upset and clinch its first trophy since 1993 in the process, but Kai Havertz and company failed to step up in Berlin.
David Alaba and Serge Gnabry put Bayern in cruise control by the interval, with a 20th DFB-Pokal triumph all but wrapped up when Lukas Hradecky fumbled Robert Lewandowski's effort over the line moments after a glaring miss by Kevin Volland.
Sven Bender headed in four minutes later to make things interesting, but Hansi Flick's side held firm before adding a fourth in an eventful finish, Lewandowski on target again before Leverkusen scored from the penalty spot.
Bayern cut through Leverkusen's press with an exceptional move in the 10th minute but Kingsley Coman failed to beat Hradecky. Yet Bayern only had to wait another six minutes for its opener, Alaba sending an exquisite free-kick into the right-hand corner.
Hradecky pulled off an outstanding stop to deny Thomas Muller, playing in his eighth DFB-Pokal final, although he was beaten when Gnabry drilled home after being released by Joshua Kimmich.
Volland was introduced as Leverkusen searched for a way back into the contest, although the substitute completely missed his attempted shot with just Manuel Neuer to beat.
Leverkusen's misery was compounded before the hour as Hradecky let Lewandowski's long-range strike slip through his grasp.
Bender took advantage of slack marking to swiftly pull one back, though it never looked likely to be enough to spark a comeback. After missing from point-blank range in the 73rd minute, Lewandowski added his second of the contest in the closing stages, lifting a delicate finish over Hradecky.
There was time for more drama, however, with Havertz hammering home from the penalty spot after Alaba's handball was spotted by VAR (video assistant referee).
Bayern's development under Flick has been outstanding and with a domestic double once again wrapped up, this feels like a team with the confidence and quality to go all the way when the UEFA Champions League resumes in August.
Bayern's players face a month-long break before they take on Chelsea in the UEFA Champions League, leading 3-0 from the first leg.
Leverkusen, meanwhile, will hope to retain its key players ahead of next season.