After a fairly uneventful opening half of football, Gervinho handed Arsenal the lead with a tidy finish after 42 minutes. However, a Kostas Mitroglou header levelled the scores just before the interval.
Arsenal were back ahead just before the hour mark when Lukas Podolski converted from close range, but both sides did have chances to add to their tally in the second period.
In the end it was Aaron Ramsey who added gloss to the scoreline with a cool finish in the final moments to wrap up the points.
Here, Sports Mole dissects the 90 minutes of action between the two Group b rivals.
On target 4
On target 5
Was the result fair?
On the balance of play, you would have to say just about. Arsenal certainly started the match the better, but they failed to create any real chances in the opening period. They had four shots on target in the 90 minutes and scored three, which explains the type of match it was. Olympiakos did impress, but they failed to really threaten late on.
5/10. This will certainly not go down as one of Arsenal's better nights in Europe. They enjoyed plenty of possession, as they so often do, but they never really created enough chances. They took the lead before the break against the run of play and the same could be said for their second strike. However, it is two wins from two Champions League matches.
5/10. It was an impressive performance from the Greek outfit. They were not expected to get anything from the match, but they played like a team that fancied their chances. They were unlucky to go behind in the opening period and had they taken their chances, it might have been different result.
Sports Mole's man of the match
Kostas Mitroglou: The 24-year-old striker grabbed an equaliser for Olympiakos before the break and was a constant menace to Arsenal in the second period. It was an impressive night from the Greek striker.
Biggest gaffe of the match
Olympiakos goalkeeper Balazs Magyeri was caught out on Arsenal's first two goals this evening. They were decent enough strikes, but they were shots that he would have been expected to save.
Svein Oddvar Moen had a fairly successful 90 minutes of action this evening. The 33-year-old was not overawed by the occasion and was prepared to hand out bookings when appropriate.
Arsenal: The Gunners return to domestic duty with a trip to West Ham United on Saturday.
Olympiakos: The Greek outfit will attempt to continue their perfect league record when they face Asteras Tripolis on Sunday.