Olympiakos edged Juventus 1-0 on Wednesday night in Piraeus after a first-half goal from Pajtim Kasami.
The Swiss midfielder struck in the 36th minute to hand his team three valuable points in the Champions League.
The outcome has left Michel's side level on six points with Atletico Madrid at the top of Group A after three games played. Atletico thrashed Malmo FF 5-0 in Spain.
Juventus failed to test Olympiakos goalkeeper Roberto Gago in the opening half but had plenty of opportunities to equalise after the re-start yet failed to convert any.
Juve encountered a hostile atmosphere at the Karaiskakis Stadium and lost to Olympiakos for the first time in Greece.
The Italians have dropped to third in the pool, three points adrift of the leaders.
Arturo Vidal returned to the starting XI for Juve after the Chilean midfielder was rested in Saturday's 1-1 draw at Sassuolo.
Alvaro Morata earned his first start for the Italians, playing alongside Carlos Tevez up front.
The hosts had the first chance of the game in the seventh minute when Alejandro Dominguez's curled effort was kept out by Juventus goalkeeper Gianluigi Buffon.
Juve almost took a 12th-minute lead when Morata headed the ball down and in the direction of Tevez.
The Argentinian's goal-bound shot was blocked by defender Omar Elabdellaoui on the goal-line with Gago already beaten.
At the other end, Luka Milivojevic's hard drive from 30 yards was tipped over the bar by Buffon.
The Italy national team captain was called on again to make a save midway through the first half and had to clear Kasami's powerful strike from long range.
Olympiakos' efforts paid off when a play started by Dominguez saw Kostas Mitroglou set up Kasami just outside the area.
He then hit the ball towards the near post and out of Buffon's reach.
Juve looked more dangerous in the second half and should have pulled level when Paul Pogba set up Stephan Lichtsteiner in the box but his effort went wide.
Before the hour mark, Juve coach Massimiliano Allegri brought on Claudio Marchisio in place of Andrea Pirlo.
Tevez was denied the equaliser in the 75th minute when his right-footed attempt was saved by Gago.
Five minutes later and Gago again came to the rescue when he kept out Morata's 12-yard shot from the centre of the box.
With four minutes remaining, Morata fed Tevez just outside the area and his powerful attempt was saved by Gago as Olympiakos held on for their second win in Group A.