Albion trail the Premier League Champions by two goals to nil.
Eden Hazard scored before there were three minutes on the clock, with a fierce drive from the edge of the area.
Three minutes later a combination of flicks and backheels between Hazard and Willian saw the latter fire an unstoppable drive past Maty Ryan.
Albion have had their chances.
With Willy Cabellero stranded, Solly March’s cross eluded Pascal Gross.
Tomer Hemed had a great chance but Cabellero clawed his header away.
Ezequiel Schelotto looked to have a great shout for a penalty but referee Jon Moss turned down his appeal.
Schelotto was so incensed that he looked like he was marching off the pitch before being stopped in his tracks by Shane Duffy. Schelotto was booked for his trouble.
Willian and Hazard have combined well to create numerous Chelsea chances.
