Alvaro Morata opened the scoring with his third of the season before N'Golo Kante fired home against his old club to make the points safe, in a match that saw Eden Hazard make his first appearance of the season for the Blues.
Antonio Conte's side had won five of their previous six away games against Leicester and started in confident fashion, buoyed by back-to-back wins over Tottenham and Everton.
Islam Slimani missed a great chance to break the deadlock and Chelsea capitalised soon afterwards, with Morata heading home from close range.
Kante slotted in his first goal in the top flight since the 4-0 thrashing of Manchester United last October to put the visitors in control, although Jamie Vardy's penalty made for a more anxious final 30 minutes than Conte would have liked.
Craig Shakespeare's side pushed hard for the equaliser but Chelsea held firm to claim a third win since their shock opening-day loss to Burnley, leaving Leicester to nurse a third defeat in four games.
Chelsea controlled the early exchanges, Morata bringing a save out of Kasper Schmeichel after just two minutes and Wes Morgan nearly turning a Victor Moses cross into his own net.
Vardy sliced wide in a rare opening for Leicester but their best chance of the half fell to Slimani, who was denied by a fine one-handed stop from Thibaut Courtois after Riyad Mahrez had led a fast break.
Leicester finished the half in encouraging fashion with a succession of corners but Conte's side seized control of the match five minutes after the restart, as Antonio Rudiger teed up Kante to drill right-footed into the bottom-left corner of the net with unerring accuracy from 25 yards out.
Courtois gave Leicester a lifeline just after the hour mark, bringing down Vardy as he slid to intercept the ball at his near post, allowing the England striker to fire home from the penalty spot despite the Belgium goalkeeper getting a touch.
Chelsea had penalty appeals of their own waved away by referee Lee Mason when Demarai Gray made contact with the ball with his arm while challenging Moses, with the visitors looking eager to restore their two-goal cushion and make the points safe.
Conte threw on fit-again Hazard and gave a debut cameo to Davide Zappacosta, who almost fired home a third from a tight angle before Willian wasted a wonderful opportunity to get on the scoresheet late on.
That miss proved costly for Shakespeare's side as, less than two minutes later, Chelsea found the breakthrough. Cesar Azpilicueta created space down the right and clipped a cross towards the edge of the six-yard box, where Morata made no mistake in heading firmly past Schmeichel.
