The French manager was stranded on high as he completed his European touchline ban, viewing the game alongside his boss, chief executive Ivan Gazidis, while coach Pat Rice dictated team matters from the dug-out.
Thankfully, for Wenger, he could talk to the man who employs him with some confidence as the victory was secured through early goals from two of his summer signings — teenager Alex Oxlade-Chamberlain and Brazil international defender Andre Santos.
But this game could easily have gone the same way as Arsenal’s opening European match when they conceded a late goal to end up with just a draw against Borussia Dortmund.
For what the Greeks lacked in defence, they made up for going forward and Arsenal conceded a poor goal to give Olympiakos a genuine chance of salvaging something from their trip to north London .
Rice was delighted to have finished his spell in charge unbeaten, for the second time in his Arsenal career, following a three-match winning streak just before Wenger started at the club.
“I never wanted to be a manager and I am happy being a coach,” Rice smiled afterwards. “I think Arsene was harshly treated [to be banned] and we will be happy to have him back [for our next game].
“It was just important to win this match and get closer to qualifying for the next stage of the competition. You can’t say we had all the game and, in fairness, they did well.”
Wenger was initially banned for his furious reaction to Arsenal’s narrow exit against Barcelona last season, but Arsenal will need a footballing miracle to get close to the Spanish and European champions again this season.
Olympiakos are no Barcelona, of course, and after forcing the first chance they allowed Oxlade-Chamberlain too much space when stand-in central defender Alex Song chipped the ball forward in the eighth minute.
The England under-21 international signed for £12m from Southampton controlled the ball towards goal, shrugged off a couple of half-hearted challenges and finished with the calmest of low left foot shots from about 12 yards out.
Having turned 18 last month he is now Arsenal’s youngest English scorer in European competition and clearly has a very bright future ahead of him.
Rice added: “He knows his own mind, is strong, has pace and can go inside and outside — now all he needs is consistency.”
But Arsenal’s defensive frailties were never far from the surface and Olympiakos should have equalised before they conceded a second goal after 20 minutes. This time Santos sauntered down the left wing and when his low cross was not converted by the consistently wasteful Marouane Chamakh he latched on to the loose ball and scored from an angle with a right foot shot to mark another Champions League debut goal.
This was not a meeting of Champions League heavyweights, however, and Olympiakos were right back in it only eight minutes later when Arsenal allowed Ariel Ibagaza to cross unhindered and David Fuster to head in unmarked.
Olympiakos manager Ernesto Valverde said: “We were left disappointed because we thought we could get a draw. We leave here with a bitter taste.”
Suddenly Arsenal were hanging on and keeper Wojciech Szczesny, still furious with the ease that Olympiakos had scored, tipped over a cracking effort from Djebbour.
The Polish keeper pretty much kept Arsenal in the game going into half-time, but Arsenal came out stronger after the break.
Olympiakos captain Vassilis Torosidis hit the cross bar as they threatened to wipe out Arsenal’s lead entirely and Rice responded by sending on Aaron Ramsey and fellow substitute Robin van Persie, though their lead still looked far from secure.
They were just about good value for their win in the end though they will have done little to worry any watching scouts from Tottenham ahead of their crunch Premier League trip to White Hart Lane on Sunday afternoon.
ARSENAL: Szczesny 8; Sagna 6, Mertesacker 5, Song 7, Santos 6; Rosicky 6, Frimpong 6, Arteta 7, Oxlade-Chamberlain 7(Ramsey 67, 6), Arshavin 5; Chamakh 5 (Van Persie.
OLYMPIAKOS: Costanzo 7; Torosidis 7, Mellberg 7, Marcano 6, Holebas 5; Fejsa 6, Orbaiz 6 (Modesto 75); David Fuster 8 (Pantelic 80), Ibagaza 6, Mirallas 6 (Abdoun 75); Djebbour 7.
Ref: Carlos Carballo (Spain).