Leading 3-1 from the game in Greece, the Gunners were comfortable throughout the first half in London.
Some nerves began to show after Youssef El-Arabi’s shot found the net via a deflection off Gabriel to give the visitors hope of repeating last season’s shock – when they knocked the Gunners out of the Europa League in the last 32 by scoring in the final minute of extra time at Emirates Stadium.
However, Olympiakos were unable to build on El-Arabi’s goal as Arsenal managed the remainder of the tie adequately to progress, helped by a red card shown to Ousseynou Ba for dissent late on.
They will discover their quarter-final opponents when the draw is made in Switzerland at 12:00 GMT on Friday.
Arsenal have developed a habit of making life hard for themselves under Mikel Arteta.
Once again, they were their own worst enemies at Emirates Stadium with a tame and occasionally sloppy second-leg display that offered the incentive to their opponents.
Thankfully for the Gunners, most of the heavy lifting for this win had been done in the first leg in Pireas, where late goals from Gabriel and Mohamed Elneny made amends for some poor defending which allowed the Greek side to briefly regain parity in the tie.
That frailty at the back resurfaced again in London, though, with Dani Ceballos’ loose pass allowing the Greek side to set up El-Arabi for his goal.
The Morocco striker could also have scored before then to offer an earlier incentive to the visitors, but Bernd Leno’s save made amends for the lax defending that allowed him to get within sight of the target from a long ball.
The poor Gunners defending was allied with a profligacy in attack.
Pepe could have settled the tie for good after beating the onrushing keeper but saw his subsequent finish from an angle deflected just wide by a covering defender.
Pierre-Emerick Aubameyang, recalled after being left out of Sunday’s north London derby win over Tottenham for breach of “pre-match protocol”, could have had a hat-trick and certainly should have taken at least one of the numerous good chances that came his way.
Arteta has called for his side to demonstrate better game management – and while the Spaniard was visibly angered by some of the choices his side made after the deadlock had been broken, he can take some satisfaction from the fact they were able to draw the sting out of the Greek champions after El-Arabi scored.
The fight had already drained somewhat from Olympiakos, but Ba’s dismissal – courtesy of a second yellow for throwing the ball down in disgust following a foul – eradicated it.
It was a far from perfect display but more than enough to ensure that the Gunners remain in the hunt for a European trophy and the sought-after prize of a Champions League place that comes with it.