PSV Eindhoven defender Alex threw Arsenal a Champions League lifeline with an own goal - then sent them crashing out with a superb late header.
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Arsenal needed to score twice to reach the last eight, and looked on course when Alex diverted Denilson's corner into his own net after 58 minutes.
Arsene Wenger's side then paid the ultimate price for missing chances.
Alex, on loan from Chelsea, headed in Edison Mendez's free-kick with eight minutes left for the vital away goal.
It meant Arsenal's season had gone into meltdown in the space of 10 days, after losing the Carling Cup final to Chelsea and being dumped out of the FA Cup at Blackburn.
And it was another triumph for former Holland international Ronald Koeman, who is fast becoming the nemesis of English clubs in the Champions League.
He was in charge of Benfica when they knocked Manchester United and Liverpool out of the tournament last season, and has now masterminded the demise of last season's Champions League finalists.
Thierry Henry was restricted to a place on the bench as he recovered from a foot injury - and it soon became clear Arsenal would need to be at their best without him against a resilient PSV side.
Kolo Toure was an unlikely source of early danger, firing wide and then forcing a block out of PSV keeper Gomez with a powerful drive after 21 minutes.
Emmanuel Adebayor wasted a good chance seconds later, when he directed a header wide after he was picked out by Cesc Fabregas' cross.
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PSV broke the shackles to almost stun Arsenal 13 minutes before the interval, Phillip Cocu heading off target when he should have done better.
And the pace of Jefferson Farfan troubled a nervous Arsenal rearguard when he almost caught Gilberto Silva in possession on the edge of the area.
PSV suffered a setback five minutes before half-time when Arouna Kone, who had hurt his knee in a challenge with Fabregas, limped off to be replaced by Ibrahim Afellay.
Arsenal desperately needed a breakthrough, and they got it in fortuitous fashion after 58 minutes.
Alex's late goal was enough to put Arsenal out of Europe
Denilson's corner forced an error from Gomez, and the unlucky Alex diverted the ball into his own net - his second Champions League own goal against Arsenal.
It was unfortunate for Alex because he was easily the game's outstanding performer.
Arsenal were suddenly rampant, with Alex making amends for his error with a crucial block from Adebayor.
Fabregas then shot over when he should have scored after he was brilliantly set up by Alexander Hleb.
PSV reminded Arsenal that they were still a threat on the hour when Edison Mendez shot wide from Jason Culina's cross.
And Arsenal were very fortunate not to concede a penalty after 64 minutes when Denilson appeared to barge Farfan to the ground, but referee Alain Hamer ignored the appeals.
Arsenal, however, were in command and Arsene Wenger attempted to ram home the advantage by sending on Henry for Julio Baptista.
He tested Gomez with a trademark free-kick - but Arsenal's night was about to take a turn for the worse.
Henry suddenly appeared to be struggling with a groin injury, and then PSV inflicted a fatal blow with eight minutes left.
Hleb needlessly fouled Xiang Sun, and Alex met Mendez's free-kick to ensure Arsenal will end a season of so much promise empty-handed.
Arsenal: Lehmann, Toure, Silva, Gallas, Clichy (Walcott 85), Ljungberg (Diaby 75), Fabregas, Denilson, Hleb, Julio Baptista (Henry 66), Adebayor.
Subs Not Used: Almunia, Djourou, Aliadiere, Traore.
Goals: Alex 58 og.
PSV: Gomes, Salcido, Alex, Feher, Sun, Culina, Mendez (Vayrynen 90), Simons, Farfan (Addo 89), Cocu, Kone (Afellay 41).
Subs Not Used: Moens, Tardelli, Marcellis.
Goals: Alex 83.
Ref: Alain Hamer (Luxembourg).