The Blues were dumped out of Europe by Manchester United in midweek, and they were stunned on 17 minutes when Peter Odemwingie got away from the defence to give the in-form Baggies the lead with a neat chip over Petr Cech.
However, the reigning champions came storming back five minutes later and Scott Carson’s failure to deal with a Florent Malouda allowed the recalled Didier Drogba to fire in the equaliser after Nick Shorey’s clearance fell invitingly to the Ivorian.
It took another four minutes for the visitors to go in front and again Carson will take some of the blame after he parried Drogba’s long-range shot straight to Salomon Kalou, who made no mistake with a swift finish.
The Blues were now on top and Frank Lampard’s effort from range was tipped over by Carson, but the Albion goalkeeper could not prevent the England man adding a third just before the break following good work from Drogba and Malouda.
Drogba then made a key goalline clearance at the other end to ensure his side remained two goals to the good, and they could have had more as the second half progressed.
Carson did well to save from Malouda before Kalou was denied by the crossbar, and substitute Fernando Torres’ frustrations continued when he rounded Carson and slotted home only to see his first ‘goal’ for Chelsea ruled out by the offside flag.
The unmarked Spaniard then wasted another fine chance from Malouda’s free-kick but the Blues had done more than enough to claim the three points.