Tomas Rosicky's neat first-time finish allowed Arsenal to take a narrow lead into the break, but goals from Ioannis Maniatis and Kostas Mitroglou midway through the second half gave the hosts their second victory of the campaign and some encouragement ahead of their Europa League participation.
Defeat means Arsenal finish second in the group having failed to capitalise on Schalke's draw with Montpellier.
With qualification already secure for the knockout stages, if not top spot, Arsene Wenger made seven changes from the weekend defeat to Swansea. Defender Jernade Meade, 20, was handed his Champions League debut, while the Arsenal boss packed his bench with youngsters Zak Ansah, Sead Hajrovic, Elton Monteiro and 17-year-old English striker Chuba Akpom.
Gervinho and Alex Oxlade-Chamberlain both wasted early openings by shooting wide of the target before the hosts had their first opportunity in the 11th minute, when Djamel Abdoun's cutback was cleared by Thomas Vermaelen to deny Rafik Djebbour a tap-in.
With both sides happy to attack, Aaron Ramsey was wasteful when Marouane Chamakh headed Oxlade-Chamberlain's cross back towards the penalty spot in the 17th minute, but the midfielder horribly miskicked an attempted first-time shot with his left foot.
A spell of Olympiakos pressure followed, with Rosicky having to kick Vasilis Torosidis' header away from the far post following a corner, before Wojciech Szczesny was forced to parry away Abdoun's 24th-minute drive from inside the box. Six minutes before half-time, however, Arsenal made the hosts pay for their missed chances.
Gervinho wasted one promising opening, but immediately regained possession on the right before driving towards the right touchline and pulling back a low pass for Rosicky, who strode on to the perfectly-weighted ball and curled it inside Roy Carroll's far post.
The goalscorer was replaced by Andrey Arshavin at the break and the Russian wasted the second-half's first opportunity when he directed a free-header over the crossbar after Chamakh's fine delivery from the right.
Arshavin hit the target just after the hour mark to round off a fine Arsenal counter-attack, but the substitute's well-struck shot from a tight angle was parried away by Carroll on its way towards the roof of the Northern Ireland keeper's net.
Olympiakos capitalised on a questionable decision from the officials to equalise in the 65th minute. Paulo Machado's header appeared to glance the post on its way behind Szczesny's goal, but a corner was awarded to the hosts, with the keeper accused of having finger-tipped the ball to safety. Arsenal failed to fully clear the set-piece, which resulted in Ramsey inadvertently chesting the ball to Maniatis, who poked home from close range at the far post.
The Greeks completed the turn around eight minutes later. Mitroglou, who had come off the bench only a minute earlier, was gifted time and space to turn on the edge of the box before curling a lovely low shot around Szczesny.