Jose Mourinho's side appeared to be cruising to three points when Branislav Ivanovic swept the ball into the rigging from close range after David Luiz had flicked on Willian's corner in stoppage time in the first half.
But Chelsea paid a heavy price for dropping further and further back as Anichebe - on for Morgan Amalfitano with 17 minutes remaining - arrived three minutes from the end of normal time to send Saido Berahino's cross beyond Petr Cech.
Chelsea must content themselves with a lead of two points rather than the four it seemed likely to be at half-time. They will be knocked off their perch at the top if second-placed Arsenal can overcome Manchester United at the Emirates on Wednesday night.
They can have few complaints with West Brom showing a gusto and spirit in the second half that was well worthy of a point.
Pepe Mel's side are also out of the bottom three on goal difference ahead of Sunderland. Their recovery demonstrated enough character to hint at better times ahead in the final 12 games of the season.
45+2' - IVANOVIC STRIKES: Ivanovic drives the loose ball into the net from the Luiz flick on. Couldn't miss really. Decent corner from Willian, but poor, poor marking. A seventh corner of the half. Finally Chelsea strike seconds before the break.
60' - WILLIAN SHOT: Brilliant piece of play by Willian. Gets a deflection off Dawson with the shot, but Foster stands tall to make a solid block.
70' - CHELSEA AGAIN HIT ON THE BREAK: Hazard and Torres lead the counter attack for Chelsea, but the move ends with Willian slamming a shot straight into the arms off Foster.
74' - WEST BROM PRESSURE BEGINS TO TELL: Bifouma thumps a shot across the face of goal from a West Brom corner. Probably West Brom's best chance of the night. Couldn't direct that towards the net.
76' - BRUNT CHANCE: Brunt then with a left foot shot. Real chance for Brunt, but he is a few yards wide with the effort at goal. West Brom with plenty of crosses into the area.
87' - WEST BROM EQUALISER: Anichebe rises to head into the net from the Berahino cross. A late equaliser for the home side. Would you believe it?
90+6' - TORRES APPEARS TO PUSH FOSTER: A bad-natured end to the match with rival players jostling in the West Brom box. Pushing and shoving, but the match is over.
MAN OF THE MATCH
Gareth McAuley (West Brom): A no-nonsense performance from the home central defender. Worked well alongside Craig Dawson in repelling the visiting side. West Brom will need men like McAuley in the run-in to avoid relegation to the Championship.
West Bromwich Albion remain unbeaten against Chelsea in a single Premier League season for the first time in the Premier League era.
Chelsea are now unbeaten in 11 Premier League matches (home and away).
Chelsea are now winless in three Premier League matches against West Brom (D1-L2).
Chelsea’s three-match winning streak in Premier League away matches comes to an end.
Talking point: How damaging is this result to Chelsea's title hopes? They didn't win the title when they overcame Manchester City last week, and they didn't lose it with this draw. But there is no doubt that they will be kicking themselves. They seemed to become more and more negative as the game progressed. Instead of pushing for a second goal, they seemed to hold out for a 1-0 win and paid the price. Well done West Brom, but Chelsea's mindset of holding what they had seemed to contribute to their own downfall.
West Bromwich Albion: Foster 7, Reid 6, McAuley 8, Dawson 8, Ridgewellm 7, Yacob 6, Amalfitano 6, Morrison 7, Brunt 7, Thievy 6, Berahino 7..subs: Mulumbu 6, Anichebe 8, Vydra 6
Chelsea: Cech 6; Ivanovic 7, Cahill 6, D Luiz 6, Azpilicueta 6; Ramires 6, Matic 6; Willian 7, Oscar 6, Hazard 6; Eto’o 6..subs: Mikel 6, Salah 6, Torres 6
MATCH IN A TWEET