Arsenal's Giroud rises to the challenge in Greek cauldron
Olympiakos 0-3 Arsenal
Olivier Giroud sometimes projects himself as a modern-day Greek god, with his chiselled looks and air of superiority, but the Arsenal forward left Athens with the stature of Zeus having delivered the most important hat-trick of his career to carry Arsene Wenger's team into the knockout stages.
This was a night when Wenger had challenged his players to approach their Olympiakos hurdle without thinking of the consequences, but none met the challenge quite as vigorously as Arsenal's centre-forward.
Petr Cech made his own crucial contribution with a string of saves, but Giroud stole the show.
From staring the ignominy of a group stage exit full in the face, Arsenal can now look forward to tackling Barcelona, Real Madrid and the rest when the draw for the last 16 takes place on Monday.
Wenger chose to be bold, knowing his side had to win by two clear goals, with Theo Walcott named in the starting XI having only just returned from a calf injury.
Joel Campbell, who announced himself to English football by scoring for Olympiakos in a 2-0 win against Man United two years ago, was also given the opportunity to enjoy another glorious Champions League night in Athens, while Alex Oxlade-Chamberlain surprisingly started on the substitutes' bench.
The Oxlade-Chamberlain decision was a gamble, both because of the risk of Walcott fading before the crucial final stages and also because the absence of his work-rate down the right left full-back Hector Bellerin repeatedly exposed.
Olympiakos had clearly identified the Arsenal right flank as a weakness in Wenger's team and Bellerin was given the runaround in the opening exchanges, Seba and Brown Ideye taking it in turns to take on the Spaniard and, by and large, beat him.
Walcott, too often, jogged half-heartedly back into a defensive position long after the horse had bolted.
Olympiakos fancied their chances. Felipe Pardo flashed a shot over the bar inside 90 seconds and Ideye should have scored after 12 minutes when, after escaping the plodding Per Mertesacker, he inexplicably decided to pull the ball back to the penalty spot rather than attempting to guide a right-foot shot past Cech from close range.
The home side, who had Kostas Fortounis correctly booked for diving in an attempt to win a penalty, went close again when Seba clipped a right-foot strike over from 20 yards.
Arsenal were chasing shadows, or kicking them in the case of Aaron Ramsey, who was booked for a clumsy tackle on Fortounis. They simply could not get a foothold in the game and Olympiakos' goalkeeper Roberto was a spectator until Mathieu Flamini's scuffed effort from Campbell's pass brushed the crossbar on 25 minutes.
That near-miss tilted the momentum in Arsenal's direction, however. Like a boxer who had been pummelled for three rounds, one counter-punch infused them with belief and, four minutes later, Giroud put them ahead.
It was a classic Arsenal goal. A sublime defence-splitting pass from Mesut Ozil to Aaron Ramsey resulted in the Welshman crossing from the left and Giroud met the ball with a powerful header.
Roberto fumbled the ball and allowed it to escape his grasp and bounce in at the near post, prompting a delayed reaction from the Arsenal players and supporters, who took an age to celebrate.
Arsenal were now one goal away from wrestling Olympiakos out of the driving seat, but those hopes looked to have suffered a blow when Giroud fell to the ground clutching his right ankle two minutes into the second-half.
He appeared to be in agony and was treated for two minutes, but he was able to climb to his feet gingerly before returning to the action.
And how important that proved to be, with the 29-year-old brushing himself down to score the decisive goal moments later. Once again he benefited from Ozil's vision, the German starting the move before Campbell's composed pass teed up Giroud to stroke the ball home from six yards.
Olympiakos responded, with Cech keeping out a Manuel da Costa header before denying Fortounis with a brilliant fingertip save.
And that was as good as it got for Olympiakos, with Giroud sending Arsenal through from the penalty spot, following a handball, to crown a famous night for Wenger and his team.
OLYMPIAKOS: Roberto, Elabdellaoui, Da Costa, Siovas, Masuaku, Kasami (Dominguez 72), Milivojevic, Pardo (Finnbogason 86), Fortounis, Seba (Santos Fortes), Ideye.
Subs not used: Botia, Salino, Kapino Cambiasso.
ARSENAL: Cech, Bellerín, Mertesacker, Koscielny, Monreal, Flamini, Ramsey, Walcott (Gibbs 72), Özil, Campbell (Oxlade-Chamberlain 90), Giroud (Chambers 90).
Goals: Giroud 29, 49, 67 (pen).
Subs not used: Debuchy, Gabriel, Ospina, Chambers, Iwobi.
Man of the match: Giroud
Match rating: 8/10
Referee: Nicola Rizzoli (Italy).