Cesar Azpilicueta found the net for Hiddink's side in the 20th minute with a neat finish at the far post from Branislav Ivanovic's low cross but Albion hit back when Craig Gardner took advantage after Pedro was dispossessed in midfield to fire past Thibaut Courtois from 25 yards in the 33rd minute.
Gardner's goal spurred the visitors into life and Salomon Rondon gave Chelsea supporters an almighty scare when his shot just skimmed wide of the post.
With four minutes remaining, however, McClean got the better of Courtois to sweep beyond the Belgium goalkeeper to tie it up for Tony Pulis' Baggies.
Chelsea huffed and puffed but could not find a winner as West Brom claimed a credible point at Stamford Bridge to drop to 13th where they sit three points clear of the 14th-placed Blues.
2015/16 BARCLAYS PREMIER LEAGUE - SEASON SCORES
Report by Joe Baker