The Greek Super League outfit went ahead just past the quarter-hour mark courtesy of Alexandro Dominguez's well-taken strike, before substitute Dimitris Diamantakos doubled the lead four minutes after the half-time break at BMO Field.
The victory was topped off with a stunning long-range strike from substitute Andreas Bouchalakis, who sent his shot swerving into the top-left corner of Milan's net in the 78th minute.
The result was Milan coach Filippo Inzaghi's first loss in three friendlies in charge of the San Siro club.
Michel's men impressed in the first half, and took the lead in the 16th minute after fine lead-up work from goalscorer Dominguez and right winger Mathieu Dossevi.
Milan's best opportunity of the opening period fell to Andrea Poli, however he was unable to control a quality cross from Michelangelo Albertazzi just past the half-hour mark.
Olympiacos regained control shortly after the break, though, as Diamantakos finished off a brilliant ball into the area from Arthur Masuaku on the left.
Milan almost opened their account in the 55th minute when Riccardo Saponara hit the crossbar, however it would be the closest they would come to troubling the scorers as they battled in their front third minus Mario Balotelli, who watched on from the stands.
