Arsenal moved to the top of their Champions League group after a disjointed performance saw them beat Olympiakos.
The Gunners took an undeserved lead in the first-half, with Gervinho opening the scoring from a low finish just outside the box.
The Greek champions then hit straight back through a superb glancing header by Kostas Mitroglou on the stroke of half-time.
But Arsene Wenger's side rallied after the break, with Podolski rifling the Gunners back in front.
Welsh captain Aaron Ramsey topped off the evening with a fine run and flick over Balazs Megyeni, securing Arsenal their second consecutive Champions League Group B victory.
The result sees Arsenal go two points clear at the top of the table after nearest rivals Schalke drew 2-2 with struggling French champions Montpellier.
It was a laboured display in truth, with the Gunners clearly still feeling a Premier League hangover after their weekend defeat at the hands of title rivals Chelsea.
Undone by some poor defending that has encapsulated Wenger's side over the past few seasons, there was little to suggest lessons had been learned as possession was relinquished cheaply and alarming errors were made at the back throughout a poor first-half.
Only five minutes had been played when goalkeeping rookie Vito Mannone's attempted pass to the out-of-sorts Thomas Vermaelen missed its target, prompting panic throughout the Gunners' defensive ranks.
Arsenal soon created their first chance though, with Santi Cazorla's costless-kick offering a rare opening for the hosts.
But despite Wenger employing Gunners legend Steve Bould to solve his side's defensive shortcomings, Vermaelen and Koscielny - at fault for both Chelsea goals on Saturday - were particularly unconvincing.
The Frenchman was cautioned for a reckless challenge on Paulo Machado before Vermaelen's poor clearance led to Mitroglou drawing a fine save from Mannone.
Central defence was again vacant as Machado met a Giannis Maniatis cross from the right, only to somehow smash his half-volley over the bar.
Arsenal's concerns were eased shortly before the break when the impressive Gervinho stepped past an opponent with ease, drilling in the opener following neat work from Podolski and Cazorla down Olympiakos' fragile left-handside.
However, the homeside immediately switched off, with Mitroglou outjumping the cumbersome Vermaelen to glance a brilliant and well-deserved header past Mannone from Leandro Greco's searching cross.
Serving the second match of a three-game touchline ban, Wenger looked far from happy as he watched on from the stands, with his side lacking both energy and creativity.
But his team came out for the second-half with a greater sense of purpose, as more fine work from Gervinho saw him cut back for Cazorla to side-foot wastefully wide.
The pressure was mounting on the Greek side's backline, and it swiftly told as the tireless Gervinho fed Podolski, firing a typically powerful shot through Megyeri's legs.
Bould introduced Theo Walcott and Olivier Giroud minutes later, and the pair combined well immediately, with the England winger crossing for the goal-shy France striker, who's well-timed volley flew straight at Megyeri.
Olympiakos were missing almost half of their usual first team through injury, with Diakite employed as an emergency right-back. And their lack of quality squad depth began to show as Arsenal piled forward with consumate ease.
Giroud's first-time strike was blocked by Dimitris Siovas's shoulder before Ramsey, another second-half substitute, latched on to the Frenchman's flick, outpacing Maniatis to dink in a fine finish past Magyeri.