The result was the biggest winning margin in Champions League history and means the Greeks finish bottom of the group and fail to qualify for the consolation spot in the UEFA Cup.
Juve had already qualified for the second phase but after three straight defeats in Serie A and Europe they showed no mercy as they ripped apart a woeful Greek defence.
After Serbian striker Predrag Djordjevic had forced a save out of Juve keeper Antonio Chimenti in the 10th minute, last season's Champions League runners-up took control.
David Trezeguet put them ahead in the 14th minute with a simple tap-in after being set up by midfielder Enzo Maresca.
Five minutes later, Fabrizio Miccoli worked some space for himself inside the area and fired a low, left-foot shot past Dimitris Eleftheropoulos to make it 2-0.
A straightforward counter-attack provided the third with Maresca releasing Miccoli who slipped the ball into the path of Trezeguet who converted another straightforward chance.
It was 4-0 in the 28th minute with once again the Olympiakos defence being opened up with unnerving ease.
A long ball forward from Igor Tudor found Miccoli on the left flank and his shot was parried out by Eleftheropoulos but Maresca crashed home the loose ball.
Straight after the break, Trezeguet went close to a hat-trick with a header while at the other end, Neri Castillo wasted a rare chance for Olympiakos, firing over the bar from a tight angle after he had rounded Chimenti.
MORE TROUBLE
But Juve were in no mood to settle for 4-0 and the outstanding Miccoli was unlucky not to have a second goal when his shot hit the far post, rolled across the line and came out off the other upright.
Trezeguet was injured in his attempt to convert the rebound but the arrival of Marco Di Vaio in his place merely meant more trouble for the hapless Greek defence.
The Italy international made it 5-0 with a first-time strike in the 62nd minute and then he set up fellow substitute Alessandro Del Piero to make it six from 10 metres out just moments after replacing Miccoli.
The only striker who had not found the target was Uruguayan Marcelo Zalayeta and he put that right with a firm header from a Maresca corner in the 79th minute.
To add just an extra touch of bitterness to the humiliation for the Olympiakos, their striker Castillo had an effort disallowed for offside in the 89th minute.
The result also equals Juve's record win in the European Cup, matching their 7-0 victory over Valur Reykjavik during the 1986/87 season.
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