Atromitos started the game very well, a compact defensive effort preventing Olympiakos any time and space while Dauda's pace on the counter posed a constant threat.
His moment came early in the second half when a fine team move allowed him to slot home from close range for his sixth goal in seven starting appearances for his new club.
This saw a change of tactic as Atromitos sat very deep and allowed Olympiakos onto them.
With no outlet, Atromitos struggled to get out and the pressure eventually told. Olympiakos substitute, Kostas Fortounis, delivered an excellent free-kick to set up a free header for Alaixys Romao to equalise.
Then 20 minutes from time, Fortounis headed home himself from a cross from the left.
Olympiakos had Manuel da Costa sent off late on but they held on to advance to the semi-finals. Atromitos and Dauda will be left to rue what might have been and they will now turn their attention to the Greek Super League.