In truth, Rovers should have won this game but were thwarted by poor finishing and dogged defending from their already relegated opponents.
West Brom may be down but, inspired by their noisy, superb fans, they rallied to equalise Damien Duff's 11th minute opener following a marvellous run and finish from midfielder Jason Koumas.
Blackburn threw everything at the Baggies as the game neared its conclusion, David Dunn really should have scored on 64 minutes when presented with a virtual open goal but fluffed the opportunity.
Ever-dangerous winger Duff though had handed Rovers the lead, racing onto Lucas Neill's through ball and firing beyond Russell Hoult.
Daniele Dichio missed three headed chances to equalise before Koumas beat two Rovers men and blasted into the roof of the net on 54 minutes. It broke Blackburn's run of five consecutive clean sheets at Ewood Park.
Jason Roberts escaped Martin Taylor three minutes later but Blackburn keeper Brad Friedel is not the PFA Goalkeeper of the Year for nothing, excellently blocking the Baggies striker.
Graeme Souness introduced Dwight Yorke for Hakan Sukur on the hour mark and it was his marvellous touches that almost created a winner, first for Garry Flitcroft and then Dunn.
Rovers substitute Craig Hignett thought he had won it four minutes from time when he flicked on Taylor's header but the ball dropped over the top and his side had dropped two crucial points.
Blackburn assistant boss Tony Parkes said: "The manager was very unhappy with the performance. It was very disappointing and we did not have enough urgency today."On the other hand Baggies boss Gary Megson was delighted by his side's display saying: "The players deserve great credit today, they gave it everything."