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After winning 2-0 at Athletic Bilbao in their Champions League opener, Arsenal dispatched the Greek champions at the Emirates Stadium to maintain their 100 per cent record in the league phase.
Martinelli netted in the first half and Bukayo Saka wrapped up the points in the closing moments. The north Londoners weren't at their best but still managed to grind out a seventh win from nine games in all competitions this season.
Mikel Arteta's men improved their impressive home record in the Champions League with a 10th clean sheet in their last 13 matches in the competition.
The Gunners are back in action on Saturday against West Ham as they aim to close the two-point gap on Premier League leaders Liverpool.
Olympiakos' visit was a welcome trip down memory lane for Arteta, who was up against one of his childhood coaches in Jose Luis Mendilibar.
