Darren Moore guided Albion to their first win since mid-January after Jay Rodriguez's 73rd minute header.
Baggies stopper Ben Foster made a couple of fine saves from former fans' favourite Romelu Lukaku before Rodriguez nodded home from a Chris Brunt corner.
"The boys put in a great performance against a very, very good team," said caretaker boss Darren Moore.
"They did what was asked of them this week; the planning, the preparation, the hard work on the training ground.
"We knew we'd have to do a lot of hard work off the ball and we knew we'd have to use it well when we did have it. I thought we did that.
"There were times where we could have used it better but we passed the ball well and created opportunities from open play. Credit to the players.
"I'm delighted that we've got the three points for everybody connected with the Football Club. Everybody can share in this result."