Having won last year's showpiece against the same opposition 4-2, Jurgen Klopp's men made it two final wins in succession on Wednesday as Mkhitaryan and Aubameyang ensured Robert Lewandowski's return to Signal Iduna Park ended in disappointment.
The Poland international spoke of a "special" homecoming to his former stomping ground in the build-up to the clash, but in the end his limelight was stolen by a typically high-energy display from Dortmund in front of their own support.
Bayern - Bundesliga and DFB Pokal champions last season - looked far from their imperious best as Pep Guardiola fielded a mix of first-team regulars and inexperienced youngsters.
The Spaniard had claimed in the days before the game that he had only a handful of fully fit players to choose from, and his concerns may have now grown after Javi Martinez was carried off on a stretcher in the first half after suffering a knee injury.
For Klopp, it was a promising curtain-raiser to the campaign, as they face up to the daunting task of bridging the 19-point gap that separated the two sides in the Bundesliga last season.
Xherdan Shaqiri was the first to threaten for Bayern as he brought a save out of Dortmund goalkeeper Mitch Langerak in the third minute, while Ciro Immobile - on his competitive debut for Dortmund - fired narrowly wide from 25 yards seven minutes later.
Dortmund almost took the lead in bizarre fashion in the 17th minute when Martinez's backpass had to be hacked off the line by a surprised Manuel Neuer, who then had to be alert to parry Oliver Kirch's powerful shot.
But Mkhitaryan did put the hosts in front midway through the first half, lashing beyond a static Neuer after the ball had ricocheted back into his path on the edge of the area.
Klopp's side continued to look the more dangerous, Aubameyang testing Neuer with a low drive in the 27th minute.
Bayern suffered a further blow on the half-hour mark when Martinez injured his left knee attempting an acrobatic volley and had to be withdrawn, with Dante coming on in his place.
Outgoing Dortmund captain Sebastian Kehl, embarking on the final season of his career, was next to threaten with a thumping drive after Bayern had failed to clear a corner in the 41st minute.
Neuer was the busiest man on the field, keeping out efforts in quick succession from Jonas Hofmann and Kehl as half-time approached.
Lewandowski, a peripheral figure throughout, was then thwarted by the onrushing Langerak at the other end shortly after the restart.
Dortmund were largely in control and Aubameyang delivered a telling blow in the 62nd minute when he rose above Jerome Boateng and planted Lukasz Piszczek's right-wing cross into the bottom left-hand corner to double the lead.
The Gabon international donned a Spiderman mask - pulled from his sock - in celebration, before being replaced by new signing Adrian Ramos.
Mkhitaryan and Immobile both had chances to make it a more resounding victory late on, while Langerak had to parry away David Alaba's swerving free-kick nine minutes from time as Bayern sought a late response.
Aside from that chance, though, Dortmund were relatively untroubled as they held on comfortably to claim the first silverware of the German season.
