The first two goals Raheem Sterling scored after switching from Manchester City to Chelsea enabled Thomas Tuchel's team to secure a crucial victory.
The England international calmed the home team's worries by scoring the game's first goal on 46 minutes with a 20-yard strike.
After Harvey Barnes pulled one back, Leicester will feel unsatisfied that they did not capitalise on a number of chances in a frantic end.
Sterling's two goals in the space of 16 second-half minutes ended the game.
Chelsea had to work hard for their victory after losing to Leeds 3-0 at Elland Road the previous week.
Sterling's two-goal display against Leicester was precisely why the England winger was signed from Manchester City this summer