The Greek champion started the match the better side of the two, but failed to beat Manuel Neuer despite creating a number of dangerous moments.

Pep Guardiola's side threatened via Robert Lewandowski and Xabi Alonso before the break, yet to no avail as home goalkeeper Roberto proved to be too much of an obstacle.

In-form Thomas Muller eventually opened the scoring with a cross that deceived Roberto shortly after the interval.

Guardiola cut a frustrated figure as his side initially failed to add to its tally, but Mario Gotze popped up in stoppage time to secure the points before Muller made it three from the spot, while Dinamo Zagreb's 2-1 win over Arsenal already puts Bayern top of the group.

Olympiacos did well to keep Bayern at bay in the opening stages of the game and looked the most dangerous of the two early on.  

Neuer was forced into making a save for the first time after eight minutes of play, yet Pajtim Kasami's header after Alejandro Dominguez lacked the power to really trouble the Germany goalkeeper.  

Bayern genuinely threatened for the first time after 26 minutes of play via Lewandowski. Alonso set up the Poland international with a fine free-kick, yet the striker's attempt was kept out by Roberto and Brown Ideye.

The Bundesliga champion then came close to breaking the deadlock a number of times within the space of minutes.

Muller first set up Douglas Costa in a dangerous position, but the Brazil international was denied by Roberto. Costa then found Lewandowski with a good cross, yet the striker's effort was scrambled off the line.  

Finally, Muller went for goal himself, only for Roberto to once more show his class with a sublime save. 

An opportunistic attempt from Alonso in the closing stages of the first half went inches wide as it remained scoreless at half-time.

Bayern started the second half superbly and broke the deadlock in the 52nd minute, albeit in somewhat fortunate fashion. Muller sent in a cross from the right wing toward the back post and Roberto misjudged the flight of the ball as it sailed home.

Olympiacos nearly immediately hit back, yet Ideye's powerful shot from the edge of the area after good work from Omar Elabdellaoui ended up in Neuer's arms as the chance went begging.

Leandro Salino came close to frustrating Bayern with seven more minutes on the clock after Ideye beat Jerome Boateng in the air, but the Brazilian just missed the target.

Gotze then ended the host's hopes of salvaging a draw when he made it two in the dying minutes of the game after good work from substitute Kingsley Coman.

Muller poured even more salt in Olympiacos's wounds in stoppage time when he converted a penalty after Arthur Masuaku had fouled Coman inside the area.