Albion have a precious lead against the Foxes after Neal Maupay fed a perfect ball through to Adam Lallana who scored his first goal for the club with just 10 minutes gone.
Lallana nearly had a second on 35 minutes as his glancing header from Pascal Gross’s corner hit the post.
Leicester’s best chance fell to Sidnei Tavares.
Jamie Vardy knocked the ball down to Tavares who saw his half volley pushed away by Albion keeper Robert Sanchez.
Just before half-time Lallana played a ball through to Maupay who took his chance well and scored but was adjudged offside.