With manager Arsene Wenger watching from the stands as he served the final game of his European touchline ban, the Gunners - who started with captain Robin van Persie on the bench - had raced into a 2-0 lead with a fine strike from youngster Alex Oxlade-Chamberlain and Brazil defender Andre Santos' first goal for his new club.
However, in what has become a trademark of a disappointing start to the season, Arsenal looked anything but convincing at the back, with David Fuster powering in an unmarked header before the break.
The Gunners, who head to arch-rivals Tottenham on Sunday, were happy to sit back on their lead - but were almost caught out when Olympiacos captain Vassilis Torosidis crashed a curling 25-yard effort against the crossbar.
In the end, though, Arsenal did just enough to secure their second victory of the week and restored some much-needed confidence ahead of what is sure to be a testing trip to White Hart Lane.
After a positive start by the Greeks, who had lost all of their nine previous European ties in England, with Fuster sidefooting wide, Arsenal went ahead in the eighth minute.
Alex Song, dropped back into central defence because of mounting injury problems, chipped the ball up to the edge of the Olympiacos area, where Oxlade-Chamberlain was onto it like a flash, before making the most of a ricochet off Ivan Marcano to cut inside and then drive a low shot into the bottom right corner.
Arsenal, though, were fortunate not to concede a quick equaliser when Mikel Arteta had to clear Rafik Djebbour's close-range effort off the line.
The Gunners looked to have given themselves some breathing space when Andre Santos doubled their lead on 20 minutes.
The Brazil full-back, signed ahead of the deadline from Fenerbache, burst down the left before crossing to Marouane Chamakh.
Jose Holebas made a saving tackle in the six-yard box, but the loose ball fell back to Santos, who turned Marcano before rolling his shot inside the near post.
It should have been cruise control from then on in for Wenger's men, but this season, nothing is that simple.
Arsenal failed to defend a short corner, and Ariel Ibagaza pumped the ball back into the penalty area, where Fuster arrived unmarked to plant a header past the stranded Wojciech Szczesny.
Olympiacos - who had only scored once on English soil before tonight, conceding 29 - were soon pressing again as Djebbour found room down the right channel before driving in an angled shot which Szczesny tipped over.
Tomas Rosicky, captain for the night with van Persie on the bench, then tripped Kevin Mirallas just a yard outside the penalty area, and received a yellow card for his thoughtless challenge.
The visitors continued to be positive after the restart, with Mirallas drilling wide from 22 yards.
Oxlade-Chamberlain, playing in England's third tier with Southampton last season, continued to look Arsenal's main threat, as he scampered away down the right and forced Olympiacos goalkeeper Franco Costanzo off his line to make a near-post block.
Arsenal were living dangerously, though, and the Greeks came within inches of drawing level on the hour when Torosidis cut inside to curl a brilliant 25-yard effort over Szczesny, which rattled the crossbar.
Oxlade-Chamberlain was substituted by assistant manager Pat Rice, who was calling the shots in the dugout, and left to a standing ovation on 67 minutes, Wales captain Aaron Ramsey his replacement.
Andrey Arshavin was released down the left and charged into the Olympiacos penalty area, before turning former Villa defender Olof Mellberg and bringing a save out of Costanzo.
With 20 minutes left, van Persie replaced Chamakh as the home side looked for a third to kill off the tie.
After being played at such a frantic pace, it was no surprise to see the tempo drop in the closing stages.
Rice looked to protect Arsenal's lead when he sent on England full-back Kieran Gibbs to replace Arshavin for the final seven minutes.
Despite defending deep, the Gunners were never really threatened and made it four points from their opening two Group F games.
Arsenal: Szczesny, Sagna, Mertesacker, Song, Andre Santos, Frimpong, Arteta, Rosicky, Oxlade-Chamberlain (Ramsey 67), Arshavin (Gibbs 82), Chamakh (van Persie 70).
Goals: Oxlade-Chamberlain 8, Andre Santos 20.
Olympiacos: Costanzo, Torosidis, Mellberg, Marcano, Holebas, Orbaiz (Modesto 75), Fejsa, Ibagaza, David Fuster (Pantelic 80), Djebbour, Mirallas (Abdoun 75).
Goals: David Fuster 27.