Pierre-Emerick Aubameyang and Henrikh Mkhitaryan struck within five second-half minutes of each ot...
Thomas Tuchel's men struggled to break through against their Bundesliga opponents, with Marwin Hitz making a number of key saves in the first-half for the hosts, but class shone through in the end.
Dortmund's fist came through imperious Gabonese forward Aubameyang in the 61st minute, his 27th of the season, before Armenian Mkhitaryan grabbed the second five minutes later to put the game to bed.
Dortmund will now face Stuggart in the quarter finals while Anthony Ujah's Werder Bremen face a difficult trip to Leverkusen.
DFB-Pokal quarter-final draw
Bochum v Bayern Munich
Stuttgart v Borussia Dortmund
Heidenheim v Hertha Berlin Bayer Leverkusen v Werder Bremen