A brace from Thomas Müller and Mario Götze's strike were enough to see Bayern Munich claim a hard-earned three points away in Greece.
Olympiakos, who won 3-0 at the weekend, replaced Luka Milivojević and Jimmy Durmaz with Leandro Salino and Pajtim Kasami. Bayern made just one change from their late win over FC Augsburg, with Juan Bernat returning to the starting line-up ahead of Rafinha.
Promising start for the hosts
The pair had early opportunities from set-pieces and crosses, though the hosts looked more dangerous. Alejandro Domínguez was providing plenty of service for Brown Ideye and he had a header easily held by Manuel Neuer, while the Argentine himself forced the Bayern stopper to gather a pacey cross.
The first real opportunity fell to Ideye, after a cross was deflected into the box. Jerome Boateng was caught out by the change in trajectory, though the Nigerian forward could only tamely head into the hands of Neuer; he was understandably annoyed to pass up the chance.
Bayern begin to dominate
Bayern responded immediately and came oh-so-close to opening the scoring. A free-kick from Xabi Alonso was lofted towards the back post and Robert Lewandowski came steaming in to head into the ground and underneath Roberto. The Spanish goalkeeper managed to get a vital flick before Arthur Masuaku volleyed the ball clear. Alonso followed with a shot that zipped inches past the upright moments later.
That spurred on the Bavarians and they had a real run of shots on goal, but Roberto dealt with it all. First, he made a routine save from Douglas Costa but quickly had to react to Lewandowski's volley. The 'keeper flicked out a leg to prevent the Pole from notching a deserved goal, while Alonso and Thiago had shots go just wide and blocked, respectively, just before the break. That was how it remained, with Olympiakos happier at the break.
Bayern break the deadlock
It was just a matter of time before Bayern broke the deadlock, and that was the case just six minutes after the break. Thomas Müller's cross-cum-shot turned into the perfect chip ass the ball sailed over Roberto's head and into the back of the net from all of 30 yards. The home crowd, and Müller himself, were shocked to see it head in but he certainly wasn't complaining with his tenth goal in eight games.
Olympiakos' players did not let the goal ruffle their feathers, and they went about responding in almost emphatic fashion. A quick counter saw Ideye pick the ball up on the edge of the box before unleashing a powerful drive towards the top corner. Manuel Neuer was not in the mood to be beaten, and produced a magnificent, acrobatic stop to push it over the bar.
Strong second half seals the win
Müller could have put the game beyond doubt with 20 minutes to go, this time with a more conventional effort. His volley was pushed wide by Roberto, who had enjoyed an excellent game so far. His side seemed determined to give it a real go in order to find an equaliser to make his work worthwhile but couldn't break down the stubborn Bayern defence.
That opportunity did come the way of the hosts and Leandro Salino, after Boateng ducked out of the way to let the Brazilian run through. He was one-on-one with Neuer but failed to hit the target, as he rifled the ball into the side-netting. They were made to pay late on, too, with Mario Götze's fine touch and finish adding some gloss to the score-line. He had Kingsley Coman to thank for some excellent build-up play, however.
Müller even had time to notch a up his brace, slotting home from the spot. Once again, it was Coman causing all the problems. The talented teen burst into the box and was fouled by Masuaku, and the resulting penalty was cool and collected. Bayern now will look forward to a home clash against Dinamo Zagreb, while Olympiakos travel to Arsenal.