Three goals in 13 first-half minutes did the damage as striker Jamie Vardy scored one and assisted another.
Vardy was teed up by Timothy Castagne for the opener, before he set up Kelechi Iheanacho after a driving run down the left for Leicester’s third.
Centre-back Jonny Evans had nodded in a deflected corner to make it 2-0.
In a game that had several goal-scoring opportunities, Castagne and West Brom’s Matheus Pereira also hit the woodwork in the first half.
Victory means Leicester are now four points clear of Chelsea, who occupy the final Champions League qualification spot with six games remaining. The two sides meet in the league – as well as the FA Cup final – next month.
“I am not thinking about the other teams. We have to think about ourselves. We can only control ourselves,” said Leicester boss Brendan Rodgers.
“This group will sometimes lose games but they are so honest and they want to be better. When you have that it is the dream ticket. It is all you can ask for as a coach.”
West Brom are on the brink of relegation as they remain nine points from safety and have a far inferior goal difference than 17th-placed Burnley.
Manager Sam Allardyce said his side “couldn’t cope” with Leicester, who he added are “only behind Manchester City on that performance”.
“You can see why Leicester are where they are in the league and why they are in the FA Cup final,” he added. “Leicester are a lot better than Southampton and far better than Chelsea. They are as good as the top boys.”