Chelsea stood firm to see off a late Leicester challenge as the Premier League champions climbed into the top three with a third straight victory.
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 space, drilled home a drive from 30 yards.
A foul by Thibaut Courtois gifted Leicester a penalty that Jamie Vardy converted and Leicester upped their tempo in a frenetic final few minutes.
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.