Arsenal dominated the early exchanges, with both the full-backs putting Olympiacos under the cosh in the opening quarter of the game or so.
After a few half-chances, the Gunners were deservedly ahead in the 34th minute, as Martin Odegaard scored from a thunderous long-range effort.
Arsenal, though, were fortunate to not go into half-time with the game on level terms.
David Luiz made an error and gifted the ball inside the box to Giorgos Masouras, who bizarrely missed the target from close range.
The Gunners, though, did not learn from their mistakes and post the break, as a poor ball by Bernd Leno put Dani Ceballos under pressure, with the Spaniard giving the ball away for Youssef El Arabi to equalise for Olympiacos.
Arsenal, though, did not get unnerved by the error-prone moments at the back, as late goals by Gabriel Magalhaes and Mohamed Elneny sealed all three points and handed the advantage to their side ahead of the home leg next week.
According to our ratings, Kieran Tierney and Martin Odegaard were the stand out performers last night as they both get an 8/10 rating.
Hector Bellerin, Gabriel Magalhaes, Granit Xhaka, Bukayo Saka, Willian and Pierre Emerick-Aubameyang all gets a 7/10 rating.
Thomas Partey and Dani Ceballos get a 6/10 rating.
Bernd Leno and David Luiz, who were the poorest performers get 5/10 ratings.