Early goals from summer signings Alex Oxlade-Chamberlain and Andre Santos proved enough for Arsenal to see out a narrow Champions League win.Oxlade-Chamberlain became the youngest English goalscorer in the competition when he waltzed across the penalty area to plant a low shot into the corner.Left-back Santos then cut inside to drive in a second before David Fuster headed in at a corner for Olympiakos.Mikel Arteta made a goal-line clearance as the Gunners held on for the win.The visitors had the first sighting of goal but Fuster could only shoot wide after good work on the right-hand side from Ljubomir Fejsa.But the home side were ahead in the eighth minute through 18-year-old Oxlade-Chamberlain.Alex Song launched a long ball forward from the back and the winger took it down nicely on his chest. He cut across the penalty area from the right and after one of the three defenders in his wake failed to make a meaningful clearance, the winger was able to dispatch a low left-footed finish into the far corner.Olympiakos had barely been in the Arsenal half but should have levelled in the 14th minute. A low corner was not dealt with and the ball fell to the feet of striker Rafik Djebbour, who saw his close-range effort brilliantly cleared from the goalline by Arteta.Per Mertesacker had to be at his best to stop a dangerous cross from Vassilis Torossidis reaching Djebbour, but moments later Arsenal doubled their lead through Santos.Tomas Rosicky released the left-back with a fine pass but his low cross was cut out by Ivan Marcano. However the Brazilian was able to collect the loose ball, cut inside and roll a right-footed effort past Franco Costanzo at his near post.Chamakh then spurned a great chance to kill the game off when he ran onto Andrey Arshavin's lofted through ball but shanked his shot horribly across the face of goal.And it was costly as Olympiakos pulled one back in the 27th minute.It was a dreadful goal to concede as Ariel Ibagaza was able to take a short corner and then receive the return ball in space on the left. He stood up a floated cross into the middle where Fuster arrived unmarked to steer a header into the corner.Szczesny was then called into action twice in a minute to parry fierce drives from Djebbour and Torossidis as Arsenal's back four looked all at sea.Kevin Mirallas then robbed Bacary Sagna to run into the area and draw another save from Szczesny as the Gunners held on to lead at the break.Oxlade-Chamberlain saw his attempted chip well blocked by goalkeeper Costanzo at the start of the second half.Jose Holebas was then fortunate not to be shown a second yellow card for tripping Oxlade-Chamberlain just before the hour mark - a decision which incensed the watching Arsene Wenger up in the stands.The visitors had been quiet but rattled the woodwork with a fine effort in the 64th minute.Captain Torossidis cut in from the right and floated a lovely 25-yard strike beyond Szczesny but onto the face of the crossbar.Oxlade-Chamberlain was replaced by Aaron Ramsey while Robin van Persie was given the final 20 minutes in place of Chamakh.And the home side survived without any late scares to pick up their first European win of the group stage.