Marc-Antoine Fortune had given the home side the lead but in a mad few minutes its lead was overturned as once again the Baggies fell to defeat in front of their supporters
Gylfi Sigurdsson and Danny Graham netted soon after Marc-Antoine Fortune had given the Baggies the lead inside the second half.
In an even contest the home side was denied a penalty by a clear Ashley Williams hand ball but it was made to regret a lapses in concentration so soon after taking the lead.
Swansea started the match well and saw an early Angel Rangel shot from a corner deflected wide. Gylfi Sigurdsson then won and took a free-kick from 20 yards out which hit the back netting, causing the visiting fans to celebrate prematurely.
However, the Baggies were denied an early penalty when Nicky Shorey’s ball into the area was taken off the head of Gareth McAuley by the hand of Williams but referee John Moss didn’t give the decision despite strong protests from the home players.
Graham was next to try his luck but after taking down Leon Britton’s pass and shrugging off McAuley he fired over inside the area.
The match livened up towards the end of the first half with Peter Odemwingie seeing his shot cleared off the line from Sigurdsson and Scott Sinclair going down in the area on the stroke of the whistle but referee Moss deemed there was not a foul.
The second half began with Swansea looking the more likely to score but after an opening spell of pressure it was West Brom which took the lead. Graham Dorrans’ corner was flicked on by Jonas Olsson to Fortune who took a touch and stuck it into the net.
However, in the space of five minutes the game had been completely turned on its head. 60 seconds after Fortune’s goal Swansea was level, with Sinclair feeding Neil Taylor down the left and the defender's cut back was met by Sigurdsson who hit it past Foster.
Moments later it was 2-1 as Sigurdsson was given time to deliver a low ball into the West Brom area and Graham was there to meet it before McAuley and again put it past Foster.
It was nearly a third goal but after good work from Graham down the left Nathan Dyer could only stab his low cross just wide while running in.
Back came the Baggies though and they should have equalized but after Dorrans’ effort was deflected into the path of Odemwingie six yards out he could only blaze over with Michel Vorm out of position. Morrison then tried his luck from the edge of the area but he could only stab over.
Rangel next slipped in Dyer but his shot was saved by Foster before Olsson blocked the follow-up from Sigurdsson. At the other end Fortune was allowed in by a Williams mistake but Vorm fortunately saved his shot as it crept wide.
The full-time whistle blew soon after to condemn West Brom to another home win and give Swansea a rare victory on its travels.