Sam Vokes scored a late equaliser to edge Burnley closer to Premier League survival and deny West Brom their first win since 18 March.
Vokes headed in five minutes from time, having earlier taken advantage of great work from Ashley Barnes to put the hosts ahead at Turf Moor.
Salomon Rondon had levelled with a smart turn and finish, before Craig Dawson thought he had won it for the visitors with a diving header.
But Vokes' header looped over Ben Foster to earn Burnley a point and keep the Clarets on course to successfully negotiating a top-flight season for the first time since 1974-75.