The Gunners headed into the clash knowing that only a two-goal victory, or a one-goal victory with a minimum of three goas scored, would be enough to see them progress.
In an expected hostile atmosphere, Arsenal silenced the home fans with an Olivier Giroud opener before the French international notched two more in the second-half to put his side through.
It was a complete performance from the Gunners, with centre-backs Per Mertesacker and Laurent Koscielny utterly superb while forward Joel Campbell had his best game in an Arsenal shirt.
Commenting on Twitter at the full-time whistle, Hartson, Owen and Shearer led the plaudits while Mark Lawrenson told BBC Radio Five Live how it was the perfect ‘Plan A’ performance.
“A lot of the Olympiakos fans in fairness have applauded the performance from Arsenal. It was a 'Plan A' performance. Get the goal, settle the nerves, go again and quite honestly they have won very comfortably,” the former Liverpool defender explained.
What a night! We needed that. Great stuff from Arsenal and Chelsea. https://t.co/nHl8DA6SGJ— michael owen (@themichaelowen) diciembre 9, 2015
Arsenal Magnificent tonight..— John Hartson (@JohnHartson10) diciembre 9, 2015
Arsenal can now look forward to being in the draw for the Champions League knockout stages, the 13th year in succession that they have reached the second phase.
La Liga trio Barcelona, Real Madrid and Atletico Madrid are three of five potential opponents as fellow Premier League rivals Chelsea and Manchester City can’t be drawn until the quarter-finals.