Van Persie, club skipper in the wake of Cesc Fabregas's exit to Barcelona, scored twice in a 3-0 home victory against Bolton Wanderers on Saturday - a win that helped steady the ship after the club's worst start to a Premier League campaign.
Despite that fillip there is still a long way to go before the doom-mongers disperse and anything short of victory on Wednesday against a club with an abysmal record in England would offer them more ammunition.
Olympiakos have lost all nine away games against English opposition in Europe, conceding 29 goals in the process and scoring just once - a record that suggests even an Arsenal side in transition should build on their opening draw in Dortmund with a convincing home win.
Van Persie, 28, has scored five goals already this season and Wenger believes the Dutchman, who British media reported on Monday was in no rush to extend his current deal beyond 2013, is now mature enough to lead from the front, both as a goal scorer and a motivator.
"Robin has matured from the boy who was a little bit emotionally impulsive when he arrived to the guy he is today," Wenger told Arsenal's website.
"It was difficult to predict but he is intelligent, he speaks his mind and you can talk to him as well. He takes advice and overall he has developed very well.
"I think he has a combination of leadership on the pitch. He is technically a super-talent, certainly, and you gain respect from the others. Now he has added the second part, that means speaking his mind."
In the wake of the defensive mayhem of an 8-2 defeat at Manchester United and a 4-3 loss at Blackburn Rovers, Arsenal looked far more secure against Bolton with German Per Mertesacker assuming the role of organiser at the back.
"After the four goals against Blackburn we lost a little bit of confidence but we were very proud of our performance on Saturday," he said. "We want to go on with this way of defending."
Arsenal have a formidable record at Emirates Stadium in the Champions League and Wenger knows smooth progression to the knockout rounds will depend on avoiding any upsets at home.
"In the Champions League, you need 11 points to qualify [from the group stage] - that means you have to take nine at home and two or three away," Wenger said.
"We got an interesting point in Dortmund and we know after if we do well at home, then we will qualify."
Theo Walcott's expected recovery from a knock sustained against Bolton will be a major boost for Wenger who initially thought the England flyer had suffered a serious injury.
They will definitely be without Jack Wilshere though while fellow midfielder Yossi Benayoun is unlikely to have recovered from a thigh strain.
Olympiakos head into the match in better shape than they were for their opening group match against Marseille two weeks ago when they lost 1-0 in Athens.
Ernesto Valverde's team had not played a competitive match before that game due to the fact their opening two Super League games were postponed as a result of a matc
