Leading 1-0 from the first leg, the Gunners, who put in an extremely disjointed display, were pegged back by Pape Abou Cisse's strike (53), which forced the tie to extra-time.
Arsenal thought they had snatched victory late in the second half of extra-time through Pierre-Emerick Aubameyang's stunning volley, but Youssef El Arabi popped up in the 119th minute to shock the Emirates and cap a historic night for the Greek side.
They now go into the round-of-16 draw, which will take place on Friday, while Arsenal's only remaining hope of Champions League football next season rests on a top-four finish in the Premier League, where they are seven points behind fourth-placed Chelsea with 11 games of the season remaining.
Arteta named a strong side, including Aubameyang, Nicolas Pepe, Alexandre Lacazette and Mesut Ozil as Arsenal looked to keep their Europa League challenge on track.
Granit Xhaka and Pepe had efforts blocked in quick succession in the early stages, before Pepe was hauled down right on the edge of the penalty area by Ousseynou Ba as he looked to burst through on goal.
Player ratings
Arsenal: Leno (6), Bellerin (5), Mustafi (7), Luiz (6), Saka (6), Ceballos (5), Aubameyang (6), Ozil (5), Pepe (4), Lacazette (5).
Subs: Torreira (6), Willock (6), Sokratis (6), Martinelli (6).
Olympiakos: Jose Sa (7), Elabdellaoui (7), Cisse (8), Ba (8), Tsimikas (8), Bouchalakis (7), Guilherme (7), Camara (7), Randjelovic (7), El Arabi (8), Valbuena (7).
Subs: Masouras (7), Gaspar (6), Lovera (n/a), Papadopoulos (n/a).
Man of the match: Pape Abou Cisse.
Ba was cautioned by referee Davide Massa, but Pepe could not take advantage as his free-kick failed to trouble goalkeeper Jose Sa.
The Gunners, who needed two crucial interventions from Shkodran Mustafi to thwart Olympiakos, started sluggishly and they struggled to find their fluency as Arteta watched on closely from the sidelines. Read Full Story
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