With Arsenal running out 3-0 winners over Dinamo Zagreb in the other game in Group F, Olympiacos will have to wait until next month’s clash with the Gunners for their chance to join Bayern in the last 16.
Bayern were 3-0 up after 20 minutes thanks to efforts from Douglas Costa, Robert Lewandowski and Thomas Muller, and Kingsley Coman completed the rout in the second half after Holger Badstuber had seen red for a foul on Brown Ideye.
The hosts broke the deadlock after just eight minutes when Douglas Costa rifled in from the left side of the box after Olympiacos goalkeeper Roberto Jimenez had parried a superb long-range effort from Bayern defender Jerome Boateng into the Brazilian’s path.
Bayern doubled their advantage in the 16th minute when Lewandowski slotted in his fifth Champions League goal of the season.
And the hosts made it 3-0 four minutes later when Arjen Robben unselfishly headed the ball across the face of goal for the unmarked Muller to tap in from close range.
Bayern were reduced to 10 men eight minutes into the second half when Badstuber was given his marching orders for fouling the on-rushing Ideye on the edge of the area when the former West Brom man in on goal.
Despite Olympiacos’ numerical advantage, Bayern added a fourth in the 70th minute when Coman latched onto Muller’s header before bravely nodding in from close range, taking a knock from shot-stopper Jimenez in the process.
Neuer, Lahm, Boateng, Badstuber, Rafinha, Robben (Kimmich 33), Muller,Vidal, Douglas Costa (Javi Martinez 72), Coman, Lewandowski (Benatia 56).
Roberto,Elabdellaoui (Leandro Salino 78), da Costa, Siovas, Masuaku, Kasami (Fortounis 67), Cambiasso, Milivojevic, Pardo (Hernani 67), Ideye, Seba.
Jonas Eriksson (Sweden).