Panathinaikos were held to a 1-1 draw over 90 minutes in the fifth round replay, a 65th minute goal by Dimitris Papadopoulos cancelling out Alban Bushaj's early goal for Apollon.
With the scores level after extra time, the game went to penalties. Apollon missed their first kick and Panathinaikos their first two but Nasief Morris, Ricardo Bovio and Dimitiris Salpigidis all scored to ensure a thrilling Panathinaikos win.
In the other fifth round replay PAS Ioannina, promoted this year to the second division, beat Super League side Iraklis 2-0.
The goals came in the space of two minutes just before halftime from Konstantinos Kazanaferis and Giorgios Saitiotis.
