Chelsea were humbled and humiliated at the Hawthorns as WBA grabbed all three points to add to the growing pressure on young manager manager Andre Villas-Boas.
The last time WBA beat Chelsea at the Hawthorns was March, 1979 when Danny Blanchflower was the Blues man in charge overseeing a similar 1-0 defeat.
Chelsea looked a shadow of a side that stormed to league titles in recent seasons.
Gareth McAuley fired the home side to an historic win with eight minutes to go and put a knife into Chelsea's ambitions of taking a Champions League spot for next season.
The Blues are now fifth, three points behind resurgent Arsenal.
But it was a reasonably bright start from both sides. But it looked as if they had lost the art of tackling as the game ebbed and flowed.
But on eight minutes the crowd erupted as a fierce James Morrison sliced right-footer appeared to be arrowing into the top left hand corner of the Chelsea net.
Petr Cech produced a marvellous save to flick the 25-yard drive over his crossbar. Chelsea responded by counter-attacking, and on 11 minutes, Daniel Sturridge disposed Jonas Olsson close to the Baggies byline. He chipped the ball back to the in-running Juan Mata, who, instead of taking a touch, decided a volley would do.
Sadly for the Spain midfielder he made a hash of the kick which ended up for a throw-in.
Mata made amends on 14 minutes by getting onto the end of a fine interchange of play which resulted in Ben Foster producing a smart near-post save from Mata's shot.
Marc-Antoine Fortune was next to try his luck, but his snap shot from the edge of the Chelsea area, on 18 minutes was scuffed and went wide.
Gary Cahill, the England hero in midweek almost opened the scoring for the Blues on 28 minutes, but his left footer from just inside the WBA area was charged down by Morrison.
Chelsea should have taken the lead five minutes before the break. Drogba, wide on the right, clawed the ball off Liam Ridgewell and raced forward. He sent in the perfect defence-splitting ball for Sturridge.
But the England forward fluffed his audition, taking too many touches instead of a first- time shot and ending up screwing his shot wide of Foster's goal.
Fortune almost hit the first goal deep into injury time as his mazy run into the box ended with a curler deflected luckily for the visitors for a corner.
There was no changes at half-time but on 57 minutes Gabriel Tamas replaced injured Steven Reid.
Fortune forced Cech into a punch out on 60 minutes as the home side started to turn the screw.
When in doubt, Villas-Boas looks to Florent Malouda to stem the tide. And so it proved, when the French winger entered the fray on 64 minutes for Sturridge. Malouda took to the left side, with Mata taking in the so-called number 10 slot, just behind Drogba.
Cech was called into action twice within a minute preventing strikes from Youssouf Mulumbu and Fortune getting through as
Chelsea's rearguard went walkabout. Ashley Cole, on 70 minutes, produced a fine intercepting header to thwart Morrison from latching onto a left wing cross as WBA piled on the pressure.
In an act of seeming desperation to snatch all three points Villas-Boas turned to misfit hit man Fernando Torres, who replaced Michael Essien on 77 minutes.
Torres last scored a goal for the Blues on October 19, 2011 when he notched a goal against Genk in the Champions League.
But the home side got what they deserved with eight minutes remaining.
Chelsea, will all 11 men back defending a corner failed to pick up Gareth McAuley who tucked home from six yards out after latching ontogeny unmarked Ridgewell's right-footer.
Villas-Boas responded by bringing on Raul Meireles for Ivanovic.
Despite a late rally from Chelsea, Foster was not unduly troubled as the home fans cheered their side to a win which must now call into serious doubt the ability of Villas-Boas to get his charges into the coveted fourth spot in the league. Teams: Cech, Ivanovic, Cole, Luiz, Essien, Ramires, Lampard, Mata, Drogba, Sturridge, Cahill Subs: Turnbull, Romeu, Torres, Mikel, Malouda, Meireles, Hutchinson. WBA : Foster, Olsson, Ridgewell, Morrison, Andrews, Reid, Thomas, Mulumbu, McAuley, Odemwingie, Fortune Subs: Fulop, Long, Brunt, Dorrans, Shorey, Tamas, Cox Ref Phil Dowd. Ends