Bayern Munich star Robert Lewandowski continued his goal scoring exploits with another hat-trick against Dynamo Zagreb as the German giants ran out 5-0 winners at home.
English clubs, however, had a bad day at the office as both Arsenal and Chelsea succumbed to defeats in their respective matches.
Olympiakos took a shock lead at the Emirates in the 33rd minute as Felipe Pardo’s shot, which was deflected off Chamberlain to wrong foot David Ospina.
Arsenal, however, equalized in a couple of minutes when Theo Walcott finished off an Alexis Sanchez through ball. Ospina handed the lead to the Greek side as the Colombian accidently took the ball into his own goal just before half-time.
Arsenal came back strong in the second half and equalizing as their Chilean talisman Sanchez headed the ball in with 25 minutes left on the clock.
Olympiakos then shocked the home team with a goal just two minutes after Sanchez had scored and held on till the end to leave Arsenal with no points after two matches in the Champions League.
Douglas Costa got the party started at the Alliance Arena with a low hard finish at the near post in the 13th minute.
Thiago Alcantara then set up Robert Lewandowski to double the lead for Bayern. Mario Goetze made it three with a low hard finish that the keeper was unable to keep out before Lewandowski doubled his personal tally with an instinctive finish that went in off the post.
As the game restarted after the break, it took Lewandowski just ten minutes to complete his hat-trick with a delicate chip over the onrushing Zagreb keeper.
The Polish international has now scored an astonishing ten goals in a week.
Bayern will head off to the Emirates next to face Arsenal who are in dire need of a win after their disastrous result against Olympiakos.
Porto maintained their great result against English sides at the Dragao with a 2-1 win over English Champions Chelsea.
Porto took the lead through Andre Andre before Willian scored his second free kick in the week after wrong footing Iker Casillas just before the break.
Porto, however, did score again with Maicon getting on the end of a Ruben Neves corner to beat Begovic at the near post. Ivanovic had a great chance to pull the London side level but the Captain on the day was unable to direct his header goalwards.
Bayer Leverkusen took the lead after completely outplaying the defending Champions Barcelona in the Nou Camp through Greek international Kyriakos Papadopoulos.
Javier Hernandez had a great chance to double the lead in the second half but the Mexican missed his chance by a country mile.
Barcelona, who struggled to create chances in the absence of Lionel Messi got back into the game after Bernd Leno parried a shot straight at Sergi Roberto, who put the ball into the open net. Just a minute later Luis Suarez came up with an outstanding finish to earn the Catalan side their first win in the Champions League.
In Belarus, BATE Borisov took a 3-0 lead in the first half against AS Roma and even as the latter came back in the second half with goals from Gervinho and Vasilios Torosidis, BATE were able to hold on for their first win off the campaign.
Dynamo Kyiv went top of Group G after their 2-0 win against Maccabi Tel Aviv courtesy of goals from Andriy Yarmolenko and Junior Moraes.
In Group H, Zenit St. Petersburg kept their winning streak intact with 2-1 win over Gent, while Valencia picked up their first points of the season with a 1-0 win over Lyon through a Sofiane Feghouli goal late in the first half.