A 0-0 draw after extra-time ensured the contest was decided by spot-kicks, Bayern winning 4-3 as Manuel Neuer's save from Sven Bender and Sokratis' strike against the post proved decisive, meaning Joshua Kimmich's miss went unpunished.
Bayern Munich 0 Borussia Dortmund 0 (AET, 4-3 pens)
Pep Guardiola's spell in charge of Bayern Munich came to a successful end in the DFB-Pokal final.
The victory ensures Bayern win a record 18th Pokal trophy as Guardiola finishes his three years in charge with an impressive double prior to joining Manchester City.
Dortmund are now without a major trophy for four seasons. They have lost three consecutive Pokal finals, the 2013 Champions League final and finished runners-up in the Bundesliga three times in the last four years.
Douglas Costa forced Roman Burki into a save with a left-footed drive and Aubameyang was off-target at the other end after his pace created an opening on the break as both sides struggled to threaten in a quiet first half.
Tempers flared near the dugouts shortly before half-time, with Gonzalo Castro and Ribery both booked for going head-to-head, but the Bayern winger was lucky to avoid a stricter punishment having appeared to gouge the eye of his opponent.
Both sides missed good chances early in the second half, with Robert Lewandowski stretching to divert Ribery's cross just wide and Aubameyang shooting over from a presentable opening after being found by Marco Reus.
Another effort from Lewandowski was too high when he collected possession following Muller's purposeful run, while Burki impressively saved a deflected Ribery strike.
Mats Hummels' last appearance for Dortmund before joining Bayern ended through injury and he was replaced by Matthias Ginter after 78 minutes, before Tuchel's men missed a golden opportunity to snatch a late winner.
It was again Aubameyang who had the chance, but he failed to adjust quickly enough to convert Lukasz Piszczek's cross and struck wide.
Guardiola and Tuchel urged their sides on prior to extra-time, with Erik Durm making a crucial block on Lewandowski as he prepared to pull the trigger and Henrikh Mkhitaryan dragging an effort wide in the best openings of the added period.
Penalties saw Bender thwarted by Neuer and Sokratis strike the foot of the post as Dortmund missed two of their first three efforts, but Burki's save from Kimmich gave them hope.
Thomas Muller and Douglas Costa converted for Bayern, however, to seal a 4-3 victory on spot-kicks, reducing Guardiola to tears.