The Blues went ahead when Cesar Azpilicueta turned in fellow full-back Branislav Ivanovic's low cross.
Craig Gardner's skimming shot levelled, but it seemed Chelsea had done enough when Gareth McAuley prodded Willian's cross into his own net.
But when the home defence failed to clear McClean made them pay with a pinpoint shot into the bottom corner.
The Republic of Ireland international's leveller was the final twist in an often ill-tempered game with Chelsea striker Diego Costa at the centre of several flashpoints, including a confrontation with several West Brom players after the final whistle.
Relive the action from Stamford Bridge
After only four goals in his first 21 games of the season, Costa has come to life in the wake of Jose Mourinho's departure as manager - doubling that tally in his past four appearances.
But, even at his best, the Spain international bristles with aggression as well as attacking threat.
From gliding past Jonny Evans and rifling over the top in the first minute, he was never far from incident - exchanging words and clashing shoulders with Jonas Olsson and Claudio Yacob and picking up a booking himself for a crude challenge on Craig Gardner.
He forced Boaz Myhill into a sprawling save with his side 2-1 up deep into the second half, but he could not deliver a third goal that would have killed off the contest and wrapped up the points.
A Stamford Bridge corridor bore the brunt of Costa's frustration as he punched a tunnel wall as he headed back to the dressing room.
Chelsea's title win last season - in which they were out-scored by second-placed Manchester City - was based on a steely defence.
But that, along with many other aspects of their play, has deteriorated sharply this term.
Despite the imposing pairing of John Terry and Kurt Zouma at centre-half, supported by 6ft 6in goalkeeper Thibaut Courtois, the hosts never looked comfortable when the ball was played into their box from out wide.
After allowing Craig Dawson and McClean to win headers in dangerous positions earlier in the match, their lack of conviction was punished as McClean threaded an 86th-minute shot into the bottom corner after a bout of penalty-area pinball.
That goal - combined with Pedro's cheap concession of possession and Zouma's failure to close down Gardner for West Brom's first - will give Blues interim boss Guus Hiddink plenty to muse on as he tries to shore up his rearguard and Chelsea's position in the table.
After their Boxing Day defeat by Swansea, West Brom were just three points from the relegation places, but home wins against Stoke and Newcastle followed by this point at Stamford Bridge have improved that cushion to more comfortable nine.
Tony Pulis' tactics - his side have played the highest proportion of long passes in the top-flight this season - have been criticised, but his record of never having been relegated as a manager looks unlikely to be spoiled by this typically well-drilled and solid Baggies side.
Salomon Rondon, well supported by McClean, was a willing runner in attack and the proceeds from the potential sale of the unsettled Saido Berahino might yet fund an evolution in the Baggies' style.
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Chelsea boss Guus Hiddink: "West Brom always bounce back, there is great character. It was an intense game.
"Diego Costa controls himself, he is very dangerous. The player is concentrated on his job and doing very well.
"Tony Pulis made a wise decision when he took over the role of the referee and took off Claudio Yacob. The referee forgot to do it."
West Brom manager Tony Pulis: "We are pleased. It was a tough game, you have to ride your luck and work hard and we did that.
"We were disappointed with one or two of our players because they got wound up and kept the crowd going. You have to be sensible and you have to play with your head.
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"There is a couple of weeks to go. Saido Berahino's situation is up in the air. The chairman is running the club diligently, the finances are up to him."
Former Newcastle, Liverpool and Manchester City midfielder Dietmar Hamman: "Physicality is a big part of the Premier League and it's what we like, but I think Diego Costa takes it a step too far. He's petty, he's childish, and he's a distraction not only to himself but to the team."
Chelsea have a couple of testing Premier League encounters up next, taking on Everton at home on Saturday before travelling to leaders Arsenal on Sunday, 24 January. West Brom play Southampton away in the league on Saturday, before an FA Cup third-round replay at Bristol City on Tuesday.
Match ends, Chelsea 2, West Bromwich Albion 2.
Second Half ends, Chelsea 2, West Bromwich Albion 2.
Foul by Willian (Chelsea).
Darren Fletcher (West Bromwich Albion) wins a free kick in the defensive half.
Offside, West Bromwich Albion. Craig Gardner tries a through ball, but Saido Berahino is caught offside.
Corner,  West Bromwich Albion. Conceded by César Azpilicueta.
Foul by Oscar (Chelsea).
Jonny Evans (West Bromwich Albion) wins a free kick in the defensive half.
Foul by Oscar (Chelsea).
Jonny Evans (West Bromwich Albion) wins a free kick in the defensive half.
Corner,  West Bromwich Albion. Conceded by Branislav Ivanovic.
Goal!  Chelsea 2, West Bromwich Albion 2. James McClean (West Bromwich Albion) right footed shot from outside the box to the bottom right corner.
César Azpilicueta (Chelsea) is shown the yellow card for a bad foul.
Foul by César Azpilicueta (Chelsea).
James McClean (West Bromwich Albion) wins a free kick on the right wing.
Corner,  West Bromwich Albion. Conceded by Branislav Ivanovic.
Kurt Zouma (Chelsea) wins a free kick in the defensive half.
Foul by Saido Berahino (West Bromwich Albion).
Attempt missed. Kenedy (Chelsea) left footed shot from outside the box is close, but misses to the right. Assisted by John Obi Mikel.
Attempt saved. Saido Berahino (West Bromwich Albion) right footed shot from outside the box is saved in the top right corner. Assisted by Darren Fletcher.
Attempt missed. Kurt Zouma (Chelsea) right footed shot from outside the box is high and wide to the right. Assisted by Oscar from a direct free kick.
Substitution, Chelsea. Nemanja Matic replaces Cesc Fàbregas.
Diego Costa (Chelsea) wins a free kick in the attacking half.
Foul by Gareth McAuley (West Bromwich Albion).
Attempt saved. Diego Costa (Chelsea) right footed shot from the right side of the box is saved in the bottom left corner. Assisted by Willian.
Own Goal by Gareth McAuley, West Bromwich Albion.  Chelsea 2, West Bromwich Albion 1.
Corner,  West Bromwich Albion. Conceded by Kurt Zouma.
Attempt blocked. Saido Berahino (West Bromwich Albion) left footed shot from the left side of the box is blocked. Assisted by Jonny Evans.
James McClean (West Bromwich Albion) is shown the yellow card.
Thibaut Courtois (Chelsea) is shown the yellow card.
Kurt Zouma (Chelsea) wins a free kick in the defensive half.
Foul by Saido Berahino (West Bromwich Albion).
Foul by Branislav Ivanovic (Chelsea).
Craig Gardner (West Bromwich Albion) wins a free kick in the attacking half.
Boaz Myhill (West Bromwich Albion) is shown the yellow card.
Substitution, West Bromwich Albion. Stéphane Sessegnon replaces Salomón Rondón.
Foul by Kenedy (Chelsea).
Craig Dawson (West Bromwich Albion) wins a free kick in the defensive half.
Attempt blocked. Saido Berahino (West Bromwich Albion) right footed shot from the left side of the box is blocked. Assisted by Salomón Rondón.
Corner,  Chelsea. Conceded by Gareth McAuley.
James McClean's late equaliser earned West Brom a share of the points as they refused to accept defeat at Chelsea.