The pair combined for a goal early in either half to send Jurgen Klopp's much-changed side through to fourth round of the DFB-Pokal
A first-half header from Julian Schieber set Jurgen Klopp's side on their way, before Jonas Hofmann doubled their advantage shortly after the break after pouncing on a rebound from Schieber's shot.
Marcel Ziemer came very close for the hosts in the first half as Dortmund rode their luck at times, but ultimately the third-tier outfit were unable to pull of a shock against last season's Champions League runners-up.
Dortmund named a weakened side for the clash - due largely to a growing injury list - with Mitchell Langerak starting in goal, Oliver Kirch slotting into midfield and both Schieber and Hofman named in attacking positions alongside Henrikh Mkhitaryan and Pierre-Emerick Aubameyang.
It took the Bundesliga side 19 minutes to break the deadlock at Stadion Ludwigspark, with Hofman chipping a delightful cross to Schieber, who headed home with aplomb.
Schieber then had the ball in the back of the net after an almost identical move, but his goal was ruled out for a push on his marker.
Dortmund continued to have the lion's share of attempts but it was Saarbrucken who came closest to scoring again just before the break, as Ziemer's instinctive effort from a free kick went narrowly wide after Sokratis had missed the flight of the ball.
The hosts were made to pay just four minutes into the second half. Schieber cut inside and saw his shot blocked, and his second effort was drilled straight at Hofmann, who did superbly to steer the ball into the net.
Dortmund had the game sewn up but spurned a handful of chances to extend their lead, but ultimately secured their place in the next round with minimal fuss.