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.
Dominguez played a ball out to Dossevi on the right, who picked out his team-mate with a well-weighted cross.
The number 10 controlled it with his chest, and then flicked a shot with the outside of his right boot past the left hand of Milan custodian Gabriel.
The Greek side had the better of the chances in the first 45 minutes, as David Fuster and Thanasis Papazoglou threatened via foot and head respectively.
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.
The Serie A side went into the interval with momentum too, after Bryan Cristante picked out Giampaolo Pazzini, but the striker could not connect at his attempt to volley in mid-air.
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.
Next up for the Serie A side is a clash with Manchester City in Pennsylvania on Sunday, while Olympiacos tackle Liverpool in Chicago later that day.
