On a day of farewells in the Black Country – with Roy Hodgson taking his final match as West Bromwich's head coach before assuming the England reins and Pat Rice serving as Arsène Wenger's No 2 for the last time – Arsenal might well have been waving goodbye to the Champions League proper until Laurent Koscielny exploited the third of three grave errors by goalkeeper Marton Fulop.
The 29-year-old Hungarian, a former Tottenham player deputising for Albion's injured player of the year Ben Foster, fluffed a routine punch, allowing the Frenchman to steer the ball into the net. Arsenal, who had seized an early lead through Yossi Benayoun before conceding twice in five minutes, to Shane Long and Graham Dorrans, equalised with a goal by Brazilian Andre Santos.
Unfortunately for Hodgson, whose next competitive assignment will be against France at Euro 2012, Fulop's performance, which could have served as a dictionary definition for "hapless", culminated in Koscielny's coup de grace.
Even then it took a brilliant last-ditch challenge by substitute Kieran Gibbs to prevent Albion's Billy Jones getting his shot away in the final moments, a tackle Wenger hailed as "deserving huge credit". The Arsenal manager, relieved to have finished ahead of Tottenham in third place, spoke of his pride in having qualified for the Champions League for the 15th consecutive year.
"There are only three clubs in Europe who've done that, [the other two being Real Madrid and Manchester United]" he said. "In September [actually October] we were 17th after losing four of the first seven. It was very difficult to imagine we could finish third, but we had an exceptional run after our exit from the Champions League. They showed mental solidity and unity, stayed united and came back."
Asked whether the way Robin van Persie lingered in front of the celebrating Arsenal supporters after the match could signify another farewell, Wenger said: "You can make of that what you want", although he expects the 30-goal Dutchman, a peripheral figure in this end-to-end contest, to remain at the Emirates.
Foster, who had suffered a groin strain in training after playing in all Albion's previous 37 matches on a season-long loan from Birmingham, reiterated after the match that Hodgson's appointment as England manager would not coax him out of international retirement. His replacement's first involvement in the Premier League this season proved as costly as it was comical.
As the ball ricocheted towards the Albion 18-yard area following a midfield challenge, Fulop dashed from his line. The situation invited him to put a boot through the ball. Inexplicably, he let it roll past him and attempted to turn and dive on to it, allowing Benayoun to steal in and run the ball into the open goal.
Albion's riposte was swift and impressive, also pointing to the soft centre of Arsenal's rearguard which Rice's successor, Steve Bould, will surely prioritise.
This time, as James Morrison speared a through-pass, Long gambolled through a gap between Koscielny and Thomas Vermaelen and sidefooted past Wojciech Szczesny from 19 yards. Wenger complained angrily that Long was offside but replays suggested referee Mike Jones was justified in giving the benefit of the doubt.
Failing to heed the lessons of Albion's opener, Arsenal gave Morrison a ridiculous amount of time to assess his options and chip the ball towards Dorrans, the only team-mate in an advanced position. The Scot sent a cushioned header into a space within the "D", ran on to the ball and volleyed crisply beyond Szczesny. Back came Arsenal. Youssouf Mulumbu lost possession inside the Albion half and Santos, taking possession 30 yards out, swerved all too easily past Simon Cox before unleashing a left-footed shot from 18 yards which Fulop got a hand to but failed to keep out.
The understudy's woes were not over. A corner, swung in by Van Persie, seemed eminently catchable, but Fulop elected to punch. Jonas Olsson jumped into him as he did so and Fulop's fists somehow turned the ball back towards his own goal. Koscielny reacted quickly to flick the ball into the net – and Arsenal into the Champions League.
WBA: FULOP, JONES, McAULEY, OLSSON, RIDGEWELL, COX, MORRISON, MULUMBU, DORRANS, LONG, FORTUNE
Arsenal: SZCZESNY, SANTOS, VERMAELEN, KOSCIELNY, JENKINSON, COQUELIN, SONG, BENAYOUN, ROSICKY, GERVINHO, VAN PERSIE
Scorers. West Brom: Long 11, Dorrans 15. Arsenal: Benayoun 4, Santos 30, Koscielny 54
Substitutes: WBA Andrews (Morrison, 51), Odemwingie (Cox, 73), Scharner (Dorrans, 79). Arsenal Walcott (Rosicky, h-t), Gibbs (Gervinho, 67), Ramsey (Santos, 79). Booked: WBA none. Arsenal Van Persie.
Man of the match Benayoun. Match rating 7/10.
Possession: WBA 43% Arsenal 57%.
Attempts on target: WBA 8 Arsenal 8.
Referee M Jones (Cheshire). Attendance 26,358.
Man City, Man United and Arsenal have qualified, and also Tottenham unless Chelsea win in the final.
Tottenham instead of Chelsea if Chelsea win in the final, plus Newcastle and Liverpool.