Cesar Azpilicueta's goal was cancelled out by substitute Craig Gardner before Gareth McAuley deflected Willian's cross into his own goal.
The Baggies came from behind for a second time when McClean struck four minutes from time as the visitors earned a deserved point.
Chelsea felt aggrieved and Diego Costa made his frustrations known at the final whistle by arguing with Baggies players.
Costa felt Claudio Yacob, already booked for a first-half foul, should have received a second yellow card for an off-the-ball trip on him early in the second half.
The midfielder was promptly substituted and referee Anthony Taylor was barracked by Chelsea players and supporters thereafter.
The Blues are unbeaten in six games since the departure of Jose Mourinho, but Guus Hiddink's hopes of a top-four finish receded further in front of owner Roman Abramovich and ahead of Saturday's clash with Everton.
Chelsea began well
Costa glided by Jonny Evans but shot wide and Willian fired off target either side of McClean heading off target from Darren Fletcher's cross.
James Morrison departed with an apparent hamstring problem before Azpilicueta blocked a Fletcher effort and then scored at the other end.
Azpilicueta is less than prolific, but likes scoring against West Brom.
The full-back, who netted at The Hawthorns in August, claimed his first goal at Stamford Bridge when he prodded in Branislav Ivanovic's cross at the back post.
There were holes aplenty in the visiting defence, but Chelsea's rearguard was porous too.
The Baggies breached and exposed when Pedro gave the ball away to Fletcher, who was influential for the visitors.
Fletcher prodded it to Gardner, who did the rest, shooting into the bottom corner from 25 yards.
Costa ballooned an effort over and Salomon Rondon shot just wide as both sides had chances to take an interval lead.
Pedro made his debut at The Hawthorns and inspired Chelsea to a first win of the season, but his star has faded since.
The subdued Spain winger was withdrawn for Kenedy at half-time and the Brazilian gave Chelsea much-needed pace and penetration in an increasingly disjointed contest.
Costa had no complaints when he was booked for a poor lunge on Gardner after losing control of the ball.
Kenedy next powered down the left and Costa looked to join the attack, only to tumble in front of Yacob.
The Baggies midfielder avoided punishment, prompting Chelsea complaints led by captain John Terry
Yacob did go off, substituted for Saido Berahino.
Chelsea continued to press, with a deflected Costa effort going into the side-netting.
McClean was then booked for squaring up to Thibaut Courtois as the contest became more niggly still.
Chelsea took the lead for a second time when Willian's cross deflected in off McAuley, who was under pressure from Kenedy.
Costa was denied and Kenedy shot wide before McClean equalised from the edge of the area after Chelsea twice failed to clear.
TWEET OF THE MATCH
"Why do we pay these chelsea players they r useless." - Former darts player Eric Bristow vents as Chelsea drop more points at home.
Thibaut Courtois: 6
Branislav Ivanovic: 7
John Terry: 6
Kurt Zouma: 6
Cesar Azpilicueta: 7
Jon Obi Mikel: 7
Cesc Fabregas: 6
Diego Costa: 6
Nemanja Matic: 6
Boaz Myhill: 6
Craig Dawson: 6
Jonas Olsson: 6
Gareth McAuley: 6
Jonny Evans: 7
Chris Brunt: 7
Claudio Yacob: 6
Darren Fletcher: 7
James McClean: 7
James Morrison: 5
Salomon Rondon: 6
Craig Gardner: 7
Saido Berahino: 6
Stephane Sessegnon: 6
STAR MAN Craig Gardner: On as an early substitute after Morrison went down injured, Gardner crashed in a superb equaliser and also had a hand in the second
Epitomised the determination of West Brom to take something from a niggly game.
MOMENT OF THE MATCH The move for Chelsea's first goal, started with a long ball from Fabregas to Costa, who fed Willian, with the Brazilian sending Ivanovic sprinting down the wing to ping in a cross for his fellow full-back Azpilicueta at the far post.
VIEW FROM THE BENCH Chelsea lined up with their familiar system with their full-backs given license to get forward, not least when both combined for the opening goal
West Brom were forced into an early change with Morrison's injury, but Gardner slotted into his 'number 10' role seamlessly.
MOAN OF THE MATCH Diego Costa
A familiar gripe but the Spaniard, who has returned to goalscoring form recently, was back at his antagonistic worst against the Baggies
After fluffing an early chance he decided to spend the rest of the match picking fights all over the pitch - even after the final whistle.
WHO'S UP NEXT?
Chelsea v Everton (Barclays Premier League, January 16)
Southampton v West Brom (Barclays Premier League, January 16)
Source : PA