By Chris Harris in Athens
Arsenal's Champions League dream is alive and kicking thanks to a classic team performance in Greece - crowned by an Olivier Giroud hat-trick.
The France striker chose the perfect time to score his first Arsenal treble, converting Aaron Ramsey's cross with a firm header, applying a calm finish from the impressive Joel Campbell's through-ball and slotting in a penalty after Nacho Monreal's shot was handled.
Giroud's second gave the Gunners the two-goal cushion they craved and his third sucked the life out of Olympiacos, leaving the Greek champions needing three goals of their own to deny Arsenal a place in the last 16.
They never looked capable of it and so Arsene Wenger's team march on in Europe, qualifying from their group for the 16th consecutive season.
SETTING THE SCENE
Victory by a two-goal margin, or any sort of win if they score three or more.
Arsenal knew the size of their task a while before their final Group F fixture but, after such a clumsy start to their Champions League campaign, the Gunners welcomed any chance - however slim - to avoid dropping into the Europa League.
Wenger's team could take heart from their 2-0 win at Monaco in March - a template for this test in Athens, according to the Arsenal manager. And with goals required, Wenger opted for one attack-minded change - Walcott replacing Alex Oxlade-Chamberlain in the starting line-up.
The Gunners would need patience and a ruthless streak when any opportunities came their way. And they would have to handle one of the hottest atmospheres in European football - that traditionally raucous crowd at the Georgios Karaiskakis Stadium.
Arsenal's plan was clear: score the first goal and let doubts creep into the minds of their opponents. But that went on hold while the visitors weathered an early storm.
Olympiacos, roared on by their fans, went for the jugular from the first whistle. Ideye Brown broke through on the left but Koscielny hoiked away his cut-back. Per Mertesacker made a vital intervention as the Greek champions made further inroads on the left, then Kostas Fortounis was booked for diving inside the Arsenal box.
The Gunners looked for a foothold in the game, with Campbell - a former Olympiacos loanee - prominent. But the Greeks looked the more dangerous side and, following another quicksilver break, Seba steered a volley off target.
Olympiacos were playing with the confidence of a side that had won 12 games straight in their domestic league. Still, it would only take one slick move to open them up and Arsenal managed that in the 24th minute.
Giroud released Campbell down the right and he weighed up his options before picking out Mathieu Flamini. The Frenchman met the ball well but his first-time shot flicked off Manuel da Costa and struck the crossbar.
It was a turning point. Suddenly Arsenal were in the ascendancy and they exposed Olympiacos again moments later, Giroud testing Roberto with a downward header. That served as a decent sighter for the French striker and he buried his next chance, a firm header from Ramsey's fine cross that Roberto could only help into the net.
A rare hush descended among the home fans; Arsenal were on track.
Mesut Ozil, whose trickery set up Ramsey for the assist, was finding his range, and the home side looked increasingly tense and ragged as the German began to dictate play.
Walcott was next to go close, his low shot skimming wide after a thrust through the centre had given him an excellent shooting chance. But Olympiacos regrouped and pushed forward again towards the end of the half, Koscielny diverting a cross just over his own bar.
The second half began with a scare for Arsenal, Giroud turning his ankle and requiring attention. It got decidedly better for Giroud and for Arsenal - within two minutes he was up on his feet to give Arsenal the two-goal advantage they craved.
Campbell was the catalyst, holding the ball up brilliantly under pressure in the Olympiacos box and waiting for the perfect moment to play in Giroud for a calm, low finish.
Olympiacos were rocked and Walcott almost added a third, his volley flicking off Da Costa and flying wide. Once again, Campbell was the creator with a teasing cross.
Fortounis forced a fine save from Petr Cech with a speculative effort from the edge of the box but Arsenal had the extra quality. Walcott and then Ozil just failed to find the right pass when well-placed to set up two more chances.
One more Arsenal goal would mean so much - it would leave Olympiacos needing three. And that precious third came in the 66th minute. Another spell of pressure ended with Monreal hammering in a shot. Omar Elabdellaoui blocked it with his hand and Giroud stepped up to complete his hat-trick from the penalty spot.
It sent the Arsenal bench into raptures and sucked the life out of the home fans. They knew the odds, so firmly in their favour at kick-off, were now stacked against them.
The game was up for the Greek champions. For Wenger, his players and their delighted fans, the Champions League quest goes on.
Referee: Nicola Rizzoli
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