Olympiakos' central defender Da Costa headed home a Kostas Fortounis set-piece in the 87th minute before Ideye dispossessed defender Stavros Tavlaridis and slotted home two minutes later for a final scoreline that flattered the hosts.
Panathinaikos had threatened to gatecrash Olympiakos' title celebrations after Marcus Berg’s early goal silenced a hostile Georgios Karaiskakis stadium in the 193rd showdown between Greece’s two most successful clubs.
But Olympiakos, who wrapped up their 43rd league title with six matches to spare two weeks ago, were level when Esteban Cambiasso drilled the ball home from inside the penalty area just before halftime.
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The goal was controversial because the linesman had flagged for interference by Olympiakos forward Alejandro Dominguez, who was standing in front of Panathinaikos goalkeeper Luke Steele but the referee overruled his assistant and gave the goal.
Panathinaikos’ Italian coach Andrea Stamaccioni was visibly annoyed as he made some cryptic comments which seemed to focus on the circumstances of the Olympiakos equaliser.
“I feel sorry for Greek football; we played well, but every match is decided by how many chances you convert," he told Nova Sports in a touchline interview.
"Fortunately, or unfortunately, the match was what it was; Greek football could improve further but honestly I feel sorry about it.”
Olympiakos boss Marco Silva added: “Congratulations must go to my players. They didn’t let going a goal down affect them and they showed composure, patience, and we believed that we could win it -- something which happened for us in the end.”
“The win is dedicated to the fans, the president and everyone who has been involved in what has been an amazing season.”
PAOK Salonica returned to winning ways with a 3-0 victory at Panaitolikos in their first match since coach Igor Tudor was sacked.
Greece striker Stefanos Athanasiadis scored twice and Nikos Korovesis added the third as PAOK held on to fourth spot with 41 points from 26 matches. The teams finishing second to fifth go into playoffs to decide who gets a Champions League place.
(Editing by Ken Ferris)
