Brendan Rodgers' men were wobbling after losing their previous two top-flight matches but produced a dazzling attacking display against the insipid visitors at the King Power Stadium.
First-half goals from Jamie Vardy, Jonny Evans and Kelechi Iheanacho gave West Brom a mountain to climb and Leicester kept a firm grip on the match after the break.
Third-placed Leicester, whose implosion at the end of last season cost them a Champions League place, now have a valuable four-point lead over Chelsea and West Ham, with just six games to go.
Rodgers praised Leicester's attitude, saying he was only focusing on his own team in the battle for a Champions League spot.
"Jamie Vardy has done it throughout his career and Kelechi Iheanacho is now showing his qualities -- he can still improve as he is still making too many mistakes, but he is getting in there," he told BT Sport.
"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."
James Maddison made his first start since February as the FA Cup finalists took a firm grip on the match and they could easily have scored five or six goals in a one-sided opening 45 minutes.
Sam Allardyce's West Brom had beaten Chelsea and Southampton to give themselves a glimmer of hope that they could survive but they remain in 19th spot, nine points from safety, and look doomed.