Having taken the lead through Yossi Benayoun, Arsenal went 2-1 down thanks to some poor defending and a dubious refereeing call, but goals from Andre Santos and Laurent Koscielny saw them win 3-2 and ensure a Champions League football for next season.
Here we rate the players who took part in the game.
Martin Fulop - 0
There are some days when you wish you hadn't woken up from the bed. Fulop must have felt like that on Sunday, when he was partially or completely at fault for all three of Arsenal's goals.
A moment of indecision allowed Benayoun to score early, failure to anticipate Santos' shot allowed the Gunners to equalise and a fumble from a corner allowed Koscielny to scramble the ball into the net. Take away the 'u' from his surname and you'll get exactly what the custodian was on Sunday.
Billy Jones - 4.5
Failed to mark Benayoun well throughout the game - allowing the Israeli to get to crosses and centres with far too much ease. Was a handful going forward though and troubled Santos quite a bit.
Jonas Olsson - 7.5
Gave a commanding performance at centre-back, charging down shots, cutting off through balls and ensuring Arsenal could not come with up that killer pass in the final third.
Gareth McAuley - 7
Worked well in tandem with Olsson, keeping close tabs on Robin van Persie and forcing the lethal striker wide every time he made a run at the Baggies' goal.
Liam Ridgewell - 4
His tendency to stick close to the central defenders allowed Arsenal's wide men to pump in crosses without too much trouble. Wasn't too threatening going forward and his dead ball delivery wasn't too special either.
Simon Cox (off 74') - 4
Gave away the ball too easily in midfield, allowing Arsenal to recover from dangerous positions - and failed to keep the lively Gervinho under control for most of the match.
James Morrison (off 52') - 8
Laid on the assists for both of West Brom's goals. While Shane Long looked offside for the first one, Morrison's delivery for the second was superb - allowing Graham Dorrans to get in behind the Arsenal defence and raise hopes of an unlikely win. Unfortunate to have to go off with an injury just after the interval.
Youssouf Mulumbu - 5.5
Was neat with his passing, but did struggle at times against a fluid Arsenal midfield of Benayoun, Tomas Rosicky and Gervinho. Could have helped out more in closing down the Gunners' men.
Graham Dorrans (off 79') - 7.5
His goal was superbly taken - one touch to bring down the ball and another to beat Szczesny with a hooked right-footed effort. Complemented Fortune well up-front.
Marc-Antoine Fortune - 8.5
The best player for the home side on the afternoon. Harried the Arsenal defenders for the entirety of 90 minutes, carved out some great chances for himself and worked hard to help out in defence as well. Was the epitome of what West Brom have been about this season.
Shane Long - 7
Somewhat fortunate to get away with the first goal, but Long was a threat for most of the game - making intelligent runs and keeping both Tomas Vermaelen and Koscielny on their toes. Did become less pivotal a figure as the game went on though.
Keith Andrews (on 52') - 6.5
Did a good job as replacement for Morrison. Although he's not as creative as the man he came on for, Andrews made up with his direct running and some snap shots that Szczesny had to be alert to keep out.
Peter Odemwingie (on 74') - 7
West Brom looked far more threatening as soon as the striker came on. Odemwingie pulled defenders away with his well-timed runs, and opened up spaces for his teammates to run into. Would have been a handful had he started the game.
Paul Scharner (on 79') - n.a
Wojciech Szczesny - 4
It wasn't a great day for either keeper, and although the Pole didn't have as horrible a day as his counterpart - he should have come out faster when Long was bearing down on goal, and could have done better with Dorrans' strike as well.
Carl Jenkinson - 5
Struggled at times against Dorrans, although he did recover on most occasions to clear the danger. Some of his crosses were pure quality, but it's clear the youngster needs more playing time to really become world-class. Putting on some brawn wouldn't hurt either.
Thomas Vermaelen - 6
Didn't have his best day, allowing Dorrans to nip in ahead of him as West Brom took the lead - but was good in the air which was crucial given the threat the Baggies posed from set-pieces.
Laurent Koscielny - 8.5
Ended a coming-of-age season with another full-blooded performance. Arsenal sat back after taking the lead, and it was the Frenchman who stood up, coming up with some absolutely stunning tackles to keep West Brom forwards at and scored the winner as well, adding gloss to a sparkling performance.
Andre Santos (off 80') - 7
Much like countryman David Luiz, Santos can be a joy to watch bombing forward, but is also the cause of billions of fingernails being chewed out of existence with his cavalier defending. Scored the goal that got Arsenal back on level terms, but his refusal to indulge in some no-nonsense defending saw Arsenal endure numerous nervy moments at the back.
Alex Song - 7.5
Always on the lookout for the lethal pass, and prickly as ever in midfield - the Cameroonian was a key man as Arsenal looked to soak by loads of Baggies' pressure. Released the Gunners on some threatening counter-attacks and made sure the like of Fortune, Andrews etc didn't have too much time on the ball.
Francis Coquelin - 4.5
Looked out his depth in the opening half, as the West Brom midfield overran him. Did get better as the game progressed, but needs to work on all aspects of his game to become a regular player for the Gunners.
Yossi Benyoun - 7.5
Was alert enough to capitalise on Fulop's error for the opening goal, and troubled Jones throughout with his darting runs. His main problem seems to be decision making - as he wasted some good openings after showing some superb control to create them in the first place.
Tomas Rosicky (off 46') - 5
Looked far from his effervescent best and had to be taken off at the interval to make way for Theo Walcott.
Gervinho (off 67') - 7
Was heavily involved in almost all of Arsenal attacks, but just like the rest of the season, couldn't figure out what to do with the ball in the final third. Credit for providing the Gunners with an outlet to release the pressure late on and making sure the West Brom defenders couldn't rest easy.
Robin van Perise - 5.5
Couldn't end the best season of his life with another goal, but it was his delivery that saw Arsenal score the goal that turned out to be the winner. Was kept quiet by the West Brom defence most of the time, and just couldn't get his shots on target on the few occasions he did have an opening.
Theo Walcott (on 46') - 4
Was largely ineffective - failing to either cut in to test the keeper or get his crosses in. Did win a couple of corners but overall a disappointing 45 minutes from the winger.
Kieran Gibbs (on 67') - 7.5
Made the tackle that could have earned Arsenal their Champions League place next season. Fortune slipped in Jones on the right and the latter's shot would likely have gone in had it not been for a sliding block by the left-back.
Aaron Ramsey (on 80') - n.a