The Spain striker took advantage of a mistake by a hesitant Gareth McAuley in the 76th minute to rob the defender of possession and curl a brilliant left-foot shot past Ben Foster. West Brom had looked like earning a point after restricting the Blues to just one other shot on target, a 30-yard David Luiz free-kick.
Chelsea also came close through an N'Golo Kante shot that deflected off Pedro and rolled just wide of the post. The Baggies had early chances through a Chris Brunt shot that fizzed wide and Salomon Rondon shooting across goal.
Chelsea move three points ahead of Arsenal while West Brom stay ninth.
Source: BBC Sports