Bayern Munich players celebrate after winning their Champions League group F soccer match against Olympiacos at the Karaiskakis stadium in Piraeus, near Athens, Greece, Sept 16, 2015. [Photo/Agencies]

Bayern came close to opening the scoring six minutes later when Lewandowski's goal-bound header was cleared off the line by Ideye and the striker was denied again on 35 minutes when Roberto showed great reflexes to parry away his first-time shot.

Olympiakos were by no means overwhelmed but Bayern continued to boss the rhythm of the match after halftime and the Germans finally broke the deadlock when Mueller's cross beat Roberto's despairing dive and arrowed into the top corner.

The Greek side spurned a great chance to level the scores with seven minutes remaining when Leandro Salino fired into the side netting with only Neuer to beat.

Despite further late pressure from the hosts, Bayern doubled their lead when substitute Gotze sprinted past two Olympiakos defenders and beat Roberto from an acute angle in the 89th minute.

Mueller then stroked home from the spot in the second minute of stoppage time to put the seal on the three points after another substitute, Kingsley Coman, had been fouled in the box by Arthur Masuaku.