Pajtim Kasami scored the only goal of the game with a well-taken finish into the bottom corner.
Juventus hit the bar twice after the break and were denied on multiple occasions by goalkeeper Roberto.
Here, Sports Mole takes a closer look at the events that unfolded at the Karaiskakis Stadium.
On Target 4
On Target 5
Was the result fair?
Although Olympiacos deserved to be in the lead at the break, they can consider themselves fortunate to have taken all three points by the end of the evening. The visitors had struggled to create any real openings until the hour mark, but they completely dominated the closing stages. Time and time again they worked great shooting chances, but they could not find a way past the outstanding Roberto. The goalkeeper was the difference and without him it would have been a very different story.
The Greek outfit started the game brightly and their forward players caused a number of problems for the Juventus defence. They never allowed their opponents to settle and there was no doubt that they were the better team going into the break. On the hour mark they could have doubled their lead, but Kasami put the ball wide from close range and from that moment Juventus took control. A sterling defensive effort ensured that they held on to their lead as they recorded their second win of the group stages.
Massimo Allegri will have been disappointed that his team could not test the keeper more in the first half, but after the break they had plenty of chances to find the net. Alvaro Morata, Carlos Tevez and Claudio Marchisio all came close to equalising, but they were denied by the keeper. The result will have drawn further criticism that they have been unable to transfer their domestic form into European matches and they will hoping that their missed chances won't cost them a place in the knockout stages.
Sports Mole's man of the match
Roberto: Without a doubt the best player on the pitch was Olympiacos goalkeeper Roberto. He looked simply unbeatable this evening and made some astonishing saves to preserve his team's one-goal lead. It was a masterclass from the Spaniard and he deserves all the praise that will surely come his way.
There were no real moments of controversy, but Allegri will be disappointed at the way that his team gave the ball away in the build up to Kasami's goal. They lost it far too easily inside their half of the pitch and paid the price as the Swiss international swept the ball home.
Milorad Mazic got all the big calls right this evening. He correctly disallowed a goal in the first half when Tevez was in an offside position and there can be no complaints about the yellow cards that he handed out.
Olympiacos: Olympiacos take on local rivals Panathinaikos in the Athens derby on Sunday.
Juventus: Juventus will look to maintain their lead at the top of Serie A with a home match against Palermo on Sunday.