The goals from Gabriel and Mohamed Elneny in the first leg proved decisive for the Gunners, who looked cagey and off the pace for the majority of the game.
Story of the game
The Gunners Boss named a mixed side featuring recalls for Dani Ceballos, Nicolas Pepe and Pierre-Emerick Aubameyang, whilst Gabriel Martinelli and Reiss Nelson found their way back onto the Arsenal bench.
Despite the fresh legs, it was a weary beginning to the game from both sides, with both goalkeepers making vital close-range saves to keep the score at 0-0.
Aubameyang, restored to the starting XI after being disciplined for lateness ahead of the North London derby, had an evening to forget, missing a series of chances to seal the tie even before the nervy final half-hour.
The first, when played through by Ceballos, was toe-poked over the bar from 18 yards, was one that last season's Aubameyang would have been licking his lips at.
Going in at half-time, there was a feeling that despite the goalless scoreline and sloppy play on both sides, the game was in hand.
That feeling evaporated just six minutes into the second half. Ceballos held on to the ball too long, allowing Olympiacos to counter from their own half.
The ball fell to Youssef El Arabi, the scorer of the goal that knocked the Gunners out of the nightmare tie last season. His shot from the top of the area took a wicked deflection from centre-half Gabriel, leaving Bernd Leno stranded.
Like a heavyweight boxer just up off the canvas, for the next ten minutes Arsenal held on shakily. Consistently playing themselves into trouble in their own third, and with little hold up play offered from the front-line, they could have been 2-0 down soon after.
Any serious threat of Olympiacos scoring the three goals needed to see them through the tie were extinguished in the 82nd minute, when two yellow cards in the space of ten seconds for Ousseynou Ba saw the visitors reduced to ten men.
Devoid of 11 men and any ideas, Arsenal saw out the final ten minutes to advance through to the quarter-finals of the Europa League. They await their destiny at tomorrow's draw, which will take place at 12pm in Nyon, Switzerland.