Arsene Wenger's fortnight from hell was in danger of reaching a new low when Antonio Di Natale levelled the play-off with Udinese in the first half of the second leg.
Yet, the Gunners showed the kind of character Wenger has always insisted was present - but which has so often been lacking - to turn the game on its head thanks to goals from new captain Robin van Persie and Theo Walcott and a brilliant Wojciech Szczesny penalty save.
The win eased the pressure on a beleaguered Wenger, who was spared the inevitable questions about his future which would have arisen had Arsenal failed to reach the lucrative Champions League proper for the first time in 14 years.
Wednesday's game was therefore a defining moment in the club's season and possibly the career of their manager, who has endured one of the worst fortnights of his near 15-year reign.
The Frenchman has now lost both his star players and has had to contend with a raft of injuries, suspensions and charges from the game's governing bodies.
He was at least given a stay of execution from his latest touchline ban and was in the dugout in what was 31-degree heat in the Italian north-east.
There were even rumours before kick-off, following Fenerbahce's expulsion from the competition, that Arsenal might be reinstated should they be eliminated.
But UEFA put paid to those by confirming during the game that Trabzonspor would replace their fellow Turks.
Arsenal did not start like a side uncertain of their fate, Walcott going close after skipping past Neuton and seeing a shot beaten away.
The game was wide open and Di Natale saw his first-time half-volley rightly ruled out for offside.
Arsenal continued to look a threat but they almost paid for giving Di Natale far too much room, Pablo Armero unable to get a clean header on the striker's cross.
Udinese should have been ahead midway through the half, Di Natale turning Mauricio Isla's cross onto the post from four yards.
But it was Walcott who wasted the chance of the half in the 33rd minute, Gervinho putting the ball on a plate for the first-leg matchwinner, who somehow shot straight at Samir Handanovic, the goalkeeper also blocking Van Persie's rebound.
Di Natale then tested Szczesny from the tightest of angles but the keeper could do nothing to stop the veteran striker six minutes before the break, the 33-year-old looping a brilliant header from Giampiero Pinzi's cross in off the post.
The restart saw Wenger take a chance on the fitness of Tomas Rosicky, replacing Emmanuel Frimpong, who himself had been a bold selection following his sending-off against Liverpool on Saturday.
Arsenal's surprisingly sparse away following did their best to gee up the visitors, who became involved in some needless handbags that saw Isla booked for dissent.
And they silenced the home fans completely 10 minutes in when Gervinho got the better of Medhi Benatia and squared for Van Persie to slot home from six yards.
Two minutes later, disaster appeared to strike again when Thomas Vermaelen was adjudged to have handled Di Natale's corner and Olegario Benquerenca pointed to the spot.
But Szczesny produced a wondrous one-handed save to tip the striker's penalty over the crossbar.
Udinese went for broke, allowing more space for the excellent Gervinho, who was showing just how much Arsenal will miss him when his domestic ban resumes at Manchester United on Sunday.
But it was, fittingly, Walcott who killed the contest in the 69th minute after outpacing the hapless Benatia and slotting past Handanovic.
Bacary Sagna was booked, as were Benatia, Walcott and Carl Jenkinson as tempers frayed amid the enormity of what was at stake.
Di Natale dragged wide trying to salvage some pride for the home side and also stung the palms of Szczesny with a free-kick from a tight angle after Isla was withdrawn for German Dernis.
The home fans immediately began to flock for the exit, with more than five minutes remaining, their misery compounded when Benatia was carried off on a stretcher.
Arsenal ran down the clock and they almost added a third goal when Van Persie and substitute Armand Traore both shot straight at Handanovic.