The home side rode a first-half goal and outstanding goalkeeping to a win over the Italian champion.
An outstanding second-half performance from Olympiakos goalkeeper Roberto helped earn his side a 1-0 win over Juventus on Wednesday.
With the Greek side leading thanks to Pajtim Kasami's first-half goal at the Karaiskakis Stadium in the UEFA Champions League Group A encounter, Spaniard Roberto produced a string of superb saves after the interval to ensure the home side claimed all three points.
In the space of 15 minutes midway through the second period, he made remarkable stops to deny Alvaro Morata, Paul Pogba and Carlos Tevez on what was a frustrating night for Massimiliano Allegri's men.
Former Fulham man Kasami had earlier struck a low finish into the bottom left-hand corner as Olympiakos continued its strong recent run of results at home on Europe's biggest club stage.
Over the past 12 months, Olympiakos has beaten Benfica, Anderlecht, Manchester United and Atletico Madrid on its own soil, and this result against the Italian champion represented its fifth consecutive home victory in the Champions League.
Juve, which dropped points in Serie A for the first time this season on Saturday with a 1-1 draw at Sassuolo, had Chile international Arturo Vidal back in the side after he was rested at the weekend, but the midfielder failed to have a telling impact as Olympiakos held on to move onto six points at the halfway stage in the group, three more than Juventus.
The hosts made a bright start, Kostas Mitroglou flicking a half-chance wide before Alejandro Dominguez brought a flying save out of Gianluigi Buffon with a free kick in the opening seven minutes.
Juve went close five minutes later as Tevez's stabbed effort was headed off the line by Omar Elabdellaoui as Olympiakos failed to deal with Andrea Pirlo's corner. Tevez did have the ball in the net in the 20th minute, but his header was rightly disallowed for offside as the host showed further hesitancy from a Pirlo set piece.
Ten minutes before the break, Olympiakos opened the scoring with a well-worked goal.
Dominguez led the break and played the ball to Mitroglou, who laid a pass back into Kasami - the midfielder firing left footed beyond Buffon from the edge of the penalty area.
Kasami should have doubled his and Olympiakos' tally on the hour mark, but he rolled the ball wide from six yards after being teed up by the influential Dominguez.
Juve almost took advantage of that miss five minutes later, but Roberto brilliantly parried Morata's thumping effort from eight yards.
Roberto performed heroics once more as the game entered the final quarter of an hour, clawing away Pogba's cross before keeping out Tevez's close-range effort with his legs.
With nine minutes remaining, he pulled off another outstanding save, reacting sharply to tip Morata's fierce drive onto the crossbar as Juve continued to press hard for an equalizer.
But a leveler did not arrive as the Greek side held on for a battling victory that puts it in pole position to qualify for the knockout stages.