After a slow start, Andre Villas-Boasâ€™ men kicked into gear to score their first maximum points haul of the season thanks to second half goals from Nicolas Anelka and Florent Malouda.
Shane Long, who scored on debut against Manchester United last week, opened the account for the Baggies when he pounced on some slow movement by Alex to dispossess the Brazilian before advancing into the area and slotting past Hilario at the near post in the fourth minute.
It took a while for the Blues to get going but they finally pierced the West Brom defence when Anelka squeezed his way into the area before getting the help of a deflection off Jonas Olsson ten minutes into the second half.
Chelsea were chipping away at the visitors and they finally hit the front with seven minutes remaining when right-back Jose Bosingwa made a devilish run through two Baggies defenders before supplying a inch-perfect pass to Malouda who had timed his run perfectly to the back post and slotted home for the eventual winner.
There were plenty of chances for both sides in the second half with West Bromâ€™s Paul Scharner missing out on a great chance to put away James Morrisonâ€™s 55th minute cross before keeper Ben Foster came up with a top-shelf save when Anelka shot on goal before Steven Reid did brilliantly to keep out Maloudaâ€™s effort from a close range rebound.
Somen Tchoyi forced Hilario to make a neat save with a swinging left-footer from the edge of the area just after the hour-mark and then it was Chelseaâ€™s turn to miss a perfectly good opportunity when substitute Didier Drogba mishit Branislav Ivanovicâ€™s swinging cross from the right.
Baggies latecomer Peter Odemwingie struck a volley from close range which Hilario kept out and that was enough to allow the Londoners to bank all three points after things looked dire earlier on.