Leonardo Jardim's champions went ahead in the 23rd minute through Djamel Abdoun's penalty after AEK defender Yago Fernandez was sent off for a professional foul on Kostas Mitroglou.
It came as no surprise when Mitroglou added a second for Olympiakos three minutes before the hour mark with a fine individual strike.
Goals late on from David Fuster and Mitroglou completed Olympiakos's biggest win against AEK away from home and capped a miserable night for Ewald Lienen's side, who are fast becoming isolated at the bottom of the table with just five points from 10 matches.
Olympiakos have 28 points and a five-point lead over second-placed PAOK Salonika, who ran out 2-0 winners at home against Platanias thanks to goals from Greece striker Dimitris Salpingidis and midfielder Alvez Lino.
Panionios held on to third place despite suffering a 1-0 defeat at Atromitos, but the Nea Smyrni club are now five points behind PAOK and 10 adrift of Olympiakos.
Panathinaikos, who are 16 points behind the leaders in eighth spot, travel to Corfu to face Kerkyra on Monday.