PAOK joined AEK Athens FC and Egaleo FC in the semi-finals after two goals in as many first-half minutes from Giorgos Georgiadis and Giannakis Okkas - the latter a spectacular diving header - left the home side with a mountain to climb.
Olympiakos striker Lambros Houtos missed an open goal eight minutes after the break and although he made amends with a 76th-minute header, it came far too late to prevent his side's exit from the competition.
Semi at stake
The remaining quarter-final takes place on 19 March, when second division Ethnikos Asteras FC will hope to overturn a 3-1 first-leg deficit against Aris Thessaloniki FC.
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