Albion trail to a 4th minute goal from former Manchester United defender Jonny Evans.
Albion have had few chances to equalise, the most notable blocked shots from Murray, Propper and Dunk.
The Seagulls will need to get something out of the match with many of the teams below them doing well.
The Baggies are enduring their worst run without a league win, having gone 20 games without victory.
They were the first team that Brighton managed to beat in a Premier League match.