Arsenal eased past Celtic to reach the Champions League group stage.
Eduardo's 25th-minute penalty, a contentious award after he clashed with Celtic keeper Artur Boruc, extended the Gunners' two-goal first leg lead.
Emmanuel Eboue finished a sweeping move for Arsenal's second after 53 minutes and Andrey Arshavin added another two minutes after coming on as substitute.
Massimo Donati's spectacular angled volley pulled one back for Celtic, but they now go into the Europa League.
Celtic's players accused Eduardo of diving to win the crucial penalty, but the Gunners were ultimately superior to the Scottish Premier League giants and merited the victory.
Arsenal were not at their flowing best, but demonstrated enough touches of their trademark invention to build on an impressive start to the season.
Arsene Wenger's side were without injured captain Cesc Fabregas, and Wenger also chose to leave Robin van Persie and Arshavin on the bench as they held a healthy lead from the first leg.
And they could have extended the lead inside seven minutes when the normally lethal Eduardo steered wide of an open goal from close range after Boruc had saved brilliantly from Nicklas Bendtner.
Eduardo was the central figure when Arsenal did score after 28 minutes - and he was very much the villain in the eyes of Celtic's travelling fans when he tumbled theatrically as he went around Boruc in the area.
Spanish official Mejuto Gonzalez infuriated Celtic by pointing to the spot, and Eduardo stayed cool despite the protests to send Boruc the wrong way to effectively put the tie out of the reach of Tony Mowbray's side.
Celtic thought they had given themselves a lifeline six minutes before the interval when Scott McDonald turned in Marc Antoine Fortune's cross from close range, but he was correctly ruled offside.
Arsenal ended the half in charge, with Boruc turning Eduardo's left-foot shot to safety and Bendtner heading the resulting corner from Denilson inches wide.
Aiden McGeady's ambitious effort from 25 yards flew just wide as Celtic attempted to revive the tie early in the second half - but all their hopes were snuffed out when the Gunners doubled their lead on the night after 53 minutes.
It was a goal that was typical Arsenal in creation, with Bendtner's clever flick releasing Abou Diaby. He fed Eboue, who took his time to find space and fire a low finish beyond Boruc.
With a trip to Manchester United looming on Saturday, Wenger made a double change with 19 minutes left, sending on Arshavin and Jack Wilshere for Eduardo and Eboue.
It was rewarded within two minutes when the Russian turned inside the area and slotted a composed effort past Boruc.
Donati pulled one back for Celtic with the last kick of the game, but it had no bearing on a contest that ended as a one-sided affair.