Both sides struggled to find a finishing touch before Alvaro Morata nodded in Cesar Azpilicueta's searching pass to put Chelsea ahead before half-time.
The visitors pressed home their advantage after the break as former Foxes midfielder N'Golo Kante, gifted time and space, drilled home low from 30 yards.
A foul by Thibaut Courtois gifted Leicester a penalty that Jamie Vardy converted, sparking Leicester into life in a frenetic final half-hour.
But it was Chelsea substitute Willian who came closest to adding to the scoring with a curling strike just wide of the post.
Leicester, who slip to 17th, have now lost six of their last seven home games against Chelsea.