The Blues were ahead inside seven minutes when Nemanja Matic flicked on Eden Hazard's corner for Diego Costa to smash home.
A David Luiz free-kick struck the post, before Pedro played in Hazard, who rounded Kasper Schmeichel to slot in.
Luiz hit his own post when clearing a cross, but Victor Moses' finish after a one-two with substitute Nathaniel Chalobah completed the scoring.
Leicester, who left Riyad Mahrez on the bench for the first time in 36 league games, failed to register a shot on target as they struggled to cope against Chelsea's aggressive pressing and quick passing.
They have won just two of their first eight games of the new season, while this was Chelsea's fifth victory under new manager Antonio Conte.