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By Graham Wood ATHENS, Dec 9 (Reuters) - Arsenal manager Arsene Wenger hailed Olivier Giroud's "perfect performance" as the French striker's hat-trick completed a remarkable escape act in the Champions League on Wednesday. Arsenal needed an emphatic win to leapfrog Olympiakos into second place in Group F and reach the competition's last 16 and had Giroud to thank for leading the cavalry charge in a 3-0 romp. The striker opened the scoring with a superb header in the first half, swept home to double the lead early in the second and scored from the penalty spot to complete a resounding win. Wenger was quick to pay tribute to Giroud, who stepped up manfully to the role of being Arsenal's go-to man in the absence of the injured Alexis Sanchez. "Giroud's performance was perfect," Wenger told reporters. "He showed skill and character... I always said he has something special on that front and he showed that again against Olympiakos." Arsenal's qualification completed a remarkable turnaround after they lost three of their first four games of the campaign and needed to win by any result other than 1-0 or 2-1 in their decisive group clash to finish second behind table toppers Bayern Munich. The victory preserved Arsenal's proud Champions League record, having now reached the competition's second stage in each of the last 16 seasons. Yet it was the way in which they got the result they needed despite a spate of recent injuries that had Wenger purring. "In the last few weeks, we've lost so many players -- (Alexis)Sanchez, (Santi) Cazorla among others," said the Frenchman. "Not many people gave us a chance and we have proved that we are a real team. We needed a perfect performance, to score without conceding, and it wasn't easy because Olympiakos are a good side... "We were in an escape mode before tonight. Maybe it's a lucky year for us in the Champions League, you never know." It was Giroud's first hat-trick for the club and the French striker was in celebratory mood. "It was a great time to score my first hat-trick," he said. "We all know that we have had a lot of injuries, but this year I think we still have a better team than in previous years in terms of both quality and quantity." (Editing by Toby Davis)