Nikopolidis, Greece's formidable last line of defence in their triumphant 2004 European Championship odyssey, made a series of outstanding saves and at times appeared to be playing Arsenal solo as he protected his goal with relish.
Dutchman Van Persie spent most of the night locked in a personal duel with the grey-haired stopper but eventually found a route past after 78 minutes of sweat.
Russian playmaker Arshavin put a more realistic gloss on the scoreline with a tap-in second from a suspiciously offside position four minutes from time to send Arsenal clear at the top of the group with six points.
It was tough on Nikopolidis, but serial Greek champions Olympiakos, managed by Brazilian great Zico, could have few complaints as they barely mustered an attack all night on the way to a ninth defeat out of nine away ties in England.
Zico, who took charge earlier this month, was left to clutch at straws afterwards.
Having seen his side outplayed he bizarrely focussed his frustration on UEFA's choice of match officials.
"I think there was a lack of sensitivity," he told reporters. "There was a referee from France, two French assistants and the fourth official and Arsenal have a French coach and 10 French players."
Arsenal manager Arsene Wenger praised Nikopolidis's rearguard effort but said had no doubt his side would score.
"He played like a genius in the game and that is why he has played at the top level all this time," Wenger said of the 37-year-old. "That's why he is a hero in Greece.
"We had a great first half but unfortunately we could not take advantage of it and it's difficult to maintain that pace and quality. But I always thought we would score.
"Overall we dominated them from the first to the last minute but they defended well and gave everything.
Arsenal could have been three up within 25 minutes.
Van Persie began his assault on Nikopolidis with a low shot from Gael Clichy's cut back and then Cesc Fabregas rocked the crossbar with a powerful left-foot drive before Tomas Rosicky's follow-up was beaten away by the over-worked keeper.
Nikopolidis then showed great agility to turn away Arshavin's low poke. The vociferous visiting fans behind Nikopolidis's goal at least had a close-up view of the action but their side offered nothing to suggest their dismal record in England was about to change.
Arsenal's only slight alarm in a first half of complete domination came 10 minutes before the interval when Vassilis Torosidis, scorer of the his side's goal in the 1-0 defeat of Alkmaar in their opening match two weeks ago, headed straight at the largely redundant Vito Mannone when unmarked.
Olof Mellberg's header from Olympiakos's first corner of the game shortly after the break also caused a flutter in the Arsenal defence but normal service was soon resumed as Nikopolidis again thwarted Van Persie.
Arsenal centre back William Gallas joined in the siege but he too was denied by Nikopolidis, as was Abou Diaby.
As the clock ticked down and with Olympiakos ha
