Leonardo Jardim's team put the disappointment of the midweek 2-1 home Champions League defeat by Schalke firmly behind them with a typically powerful performance, going ahead after just four minutes trough Algeria striker Rafik Djebbour.
A Jose Cholebas strike and a Dimitris Skliopidis own goal ensured the hosts were 3-0 ahead at halftime, with Djebbour adding the fourth - his sixth of the season - five minutes after the break.
Olympiakos have 12 points from four matches, three ahead of PAOK Salonika who were 3-0 winners at Skoda Xanthi on Saturday.
AEK Athens's early-season struggles continued as they suffered a 2-1 defeat at OFI Crete.
Vangelis Vlachos's team fell behind through two first-half penalties which were converted by Mrnes Sisic and Giorgos Ioannidis, with Jose Furtado pulling a goal back two minutes before halftime.
AEK have collected just one point from four matches and lie second from bottom in the standings.
Panathinaikos, who have also struggled in the opening weeks of the season and have two points from three matches, host Atromitos on Monday. (editing by Justin Palmer)