Jesualdo Ferreiria's Panathinaikos, unbeaten this season, produced a dominant display in the hostile atmosphere of PAOK's Toumba stadium, taking the lead through Cleyton's 25-yard free-kick just after the half hour.
Ghana forward Quincy drilled in a second in the 56th minute after great work down the right by Kostas Katsouranis before Sebastian Leto grabbed his eighth goal of the season with a low free-kick.
"We have to put this game in the past and focus on the Champions League match against Dortmund," said Olympiakos coach Ernesto Valverde whose team travel to Germany for their fourth Group F match needing a positive result to keep their qualification hopes alive.
"We thought the game was won at 2-0 and that was a mistake. We conceded two sloppy goals from set-pieces and we have to work on our concentration," Valverde added.
