The 18-year-old, who joined the Gunners from Southampton this summer, gave ArsÃ¨ne Wenger’s side an early lead with a well-taken finish before fellow Arsenal new boy Andre Santos made it 2-0 after 20 minutes.
David Fuster headed in a corner mid-way through the first half for the Greek champions but the home side were able to hold on to seal their first Group F victory.
“It was a really good experience for me,” said Oxlade-Chamberlain afterwards. “It’s a big step up from what I was used to last season.
“The football’s a lot quicker but I want to play at the top level and I’ve got a lot of work to do to get many more appearances in the Champions League.
“It’s always nice to score your first goal in the Champions League but the main thing was for the boys to get the three points and I’m glad we achieved that.”
Oxlade-Chamberlain, who opened his Arsenal account last week with a goal against Shrewsbury in the Carling Cup, admits he faces stiff competition for a place in Wenger’s first team.
“If I’m not aspiring to be in the squad then there’s something wrong,” he continued. “It’s a really hard squad to get into at the moment because we’ve got a lot of top quality players but I’ve just got to keep working hard every day and hopefully I’ll get in.”
Oxlade-Chamberlain took just eight minutes to net his first European goal, stroking in a fine far-post finish to edge The Gunners into the lead after being found by stand-in centre-back Alex Song.
But falling behind seemed to galvanise the visitors and the Greek side should have taken the lead after 16 minutes but Rafik Djebbour’s close-range effort was superbly blocked by Mikel Arteta on the goal-line.
Santos then burst down the left wing and rolled home the Gunners’ second 20 minutes in after his initial cross was blocked.
Despite impressing in Olympiakos’s half, Arsenal looked typically fragile at the back – and the visitors pulled one back in the 27th minute after Fuster was left completely unmarked from a corner to power a downward header past a motionless Wojciech Szczesny.
Arsenal managed to restore a degree of defensive stability after the break and Oxlade-Chamberlain saw his chip well blocked by goalkeeper Franco Costanzo soon after half time.
But it was not long before Olympiakos threatened again, this time through captain Vasilis Torosidis, whose 25-yard strike rattled the crossbar.
The Gunners, however, were able to hold on to to claim the three points, placing them second in Group F behind Marseille.
“We knew before the game that it was going to be very tough,” said Arsenal goalkeeper Szczesny. “You have to give credit to our defence for keeping the result at 2-1 because they did put a lot of pressure on us and it was a great defensive performance in the second half.
“I think we lost the ball too many times in the middle of park and that created some problems and they looked dangerous on the break. But we still looked like the better side in the second half and we deserved to win.”
Looking ahead to Sunday’s north London derby at White Hart Lane, Szczesny added: “We will have to step it up.
“You have to be at your very best to win that game but we’re confident. We’ve won two games on the bounce and hopefully we can go to White Hart Lane and get the three points there.”
Arsenal: Szczesny, Sagna, Mertesacker, Santos, Rosicky, Arteta, Oxlade-Chamberlain (Ramsey 68), Song, Arshavin (Gibbs 82), Frimpong, Chamakh (Van Persie 70).
Olympiakos: Costanzo, Mellberg, Marcano, Torosidis, Ibagaza, Fejsa, David Fuster (Pantelic 80), Holebas, Orbaiz (Modesto 75), Djebbour, Mirallas (Abdoun 75).
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