Needing to win by two clear goals, Olivier Giroud headed the Gunners into the lead, before adding a second shortly after the break.
The Frenchman then secured the victory with a third from the penalty spot, to complete his hat-trick and keep up Arsenal's record of progressing from the group stage.
Here, Sports Mole takes a closer look at the events that unfolded at the Karaiskakis Stadium.
On target: 4
On target: 5
Was the result fair?
There can be no doubts that Arsenal deserved to claim the win, and they could easily have scored even more goals to add to what was a very convincing scoreline. The Gunners weathered an early storm from the Greeks to take control of the tie, and once they went into the lead through Giroud's first-half header they never looked back as they secured the win to make it through from their group.
Having only suffered one defeat all season at the hands of Bayern Munich, the Greek champions went into the match full of confidence. They had beaten Arsenal in the previous meeting between the teams and just needed to avoid losing by a big margin to make it out of the group.
However, despite a promising start where they showed a real threat on the counter-attack, Olympiacos were undone by the class of Arsenal's forwards. They had no answer to the intelligent runs that Giroud made into the box, while Campbell and Walcott constantly pulled their back four out of position all evening.
There have been some special European displays over the years from Arsenal, and this will go down as another to add to the list. Due to a number of injury problems they were written off as they searched for a win by a two-goal margin that would see them through. However, a superb hat-trick from Giroud and a resolute defensive performance helped them silence their doubters.
There were a number of highly impressive displays, and while Giroud will take the plaudits with his goals, Joel Campbell produced one of his best performances in an Arsenal shirt. Theo Walcott and Mesut Ozil shone in the attack, while Aaron Ramsey flourished playing in a central role that he looks so comfortable in. Laurent Koscielny was also a rock at the heart of the defence and Petr Cech showed his class with a vital save in the second half from Kostas Fortounis.
Sports Mole's man of the match
Olivier Giroud: The Frenchman has been a divisive figure for Arsenal fans during his time at the club, but he showed his class by scoring a wonderful hat-trick. His aerial ability was on show for the first goal as he headed in Ramsey's cross, before a composed finish from Campbell's through-ball led to a second. He then ensured the victory with a fine penalty, and was given a huge applause from the travelling fans as he left the field in stoppage time.
There were a number of poor displays at the back from Olympiacos and their whole team must take a share of the blame for the defeat. Roberto may also feel that he should have saved Giroud's header, which he did manage to get a hand to, while Omar Elabdellaoui's handball that gave away a penalty ensured that their hopes of a comeback were over.
It was a fine performance from the experienced Italian Nicola Rizzoli, who showed that he is one of the best referees in Europe. He got all of the big decisions correct, and was right to book Fortounis for diving inside the box, before giving Arsenal a penalty for a handball.
Olympiacos: The Greeks will resume domestic duties with a Super League clash against Panetolikos at the weekend.
Arsenal: The Gunners will look to move to the top of the Premier League with a win over Aston Villa on Sunday.