New signing Pedro was among the scorers for the champions as Chelsea led 3-1 but after captain John Terry was sent off, James Morrison’s second goal meant the visitors had to cling on for three points.
Morrison missed a penalty for West Brom on 14 minutes before Pedro and Diego Costa made it 2-0 to Chelsea after half-an-hour.
Morrison pulled one six minutes later but Cezar Azpilicueto restored the advantage three minutes before the break.
Terry was sent off for pulling back Salomon Rondon nine minutes into the second half and Morrison halved the deficit five minutes later.
West Brom chased the equaliser and Rondon forced a good late save from Thibaut Courtois as Chelsea hung on to move into the top half while West Brom fall to the bottom of the table.
Later on Sunday, Manchester City, with two wins out of two, can go top if they win at Everton.
Original source: Ten-man Chelsea hang on for victory