The Foxes were the better team for long spells and Antonio Conte’s side never really looked like scoring, even after Ben Chilwell’s red card in the 68th minute.
The first half was very open and Victor Moses had an early effort blocked before Leicester took a firm grip on the game.
Chilwell set up Shinji Okazaki, who poked his shot wide before Jamie Vardy, restored to the Leicester line-up following injury, shot into the side-netting.
As City tore through the Blues defence time and time again, Matty James set up Vardy but he fired wide before Thibaut Courtois made a good save to keep Wilfred Ndidi’s header out.
When Chelsea hit back, Cesc Fabregas’ low drive was kept out by Kasper Schmeichel but Leicester continued to be the better team in the first half and Riyad Mahrez blasted a first-time shot over the bar while Vardy had another effort blocked.
Claude Puel’s side started the second half well although Mahrez was fortunate not to be booked when he dived inside the penalty area under Andreas Christensen’s challenge.
Mahrez’s deflected strike then drifted wide, with Courtois beaten, before Chelsea boss Conte made a double change just before the hour mark in an attempt to lift his side, with Willian and Pedro replacing Fabregas and Eden Hazard.
Chilwell was dismissed for two bookable offences, fouling Moses just five minutes after bringing Willian down.
Chelsea pushed for a late winner but Tiemoue Bakayoko’s poor effort flew over the bar before Schmeichel clawed Marcos Alonso’s cross away from danger in stoppage time as the Blues wasted the chance to go second.