Similarly to last season, striker Chris Wood gave the visitors the lead when converting Charlie Taylor's cross as the New Zealand international netted for the fourth league game on the bounce.
Burnley-born forward Harvey Barnes equalised after 20 minutes as the two sides went in level at the interval. The hosts then got their noses in front early in the second half when substitute Erik Pieters diverted Timothy Castagne's cross into his own net.
Full back Justin James stretched City's lead just after the hour when afforded a free shot on goal from close range courtesy of Ayoze Perez's centre while Jimmy Dunne, on his Premier League bow, headed past Kasper Schmeichel from Dwight McNeil's set-piece to give Burnley hope.
However, Dennis Praet eased the nerves and secured the points for the home side when thumping the ball past Nick Pope from the edge of the penalty area in the 79th minute.
1. Nick Pope 6
Nothing he could do for any of the home side's goals as the England international was left completely exposed. Communication was good, constantly barking orders and instructions to his team-mates, and made a smart save to keep out a Barnes curler.
2. Phil Bardsley 5
The full back was pushed to his limits by Harvey Barnes, who was arguable Leicester City's man of the match. Allowed the forward to get an effort away on goal in the first half when retreating, but battled well on the whole.
3. Jimmy Dunne 7
Didn't look out of place on his Premier League debut. Scored on his bow with a header from McNeil's set-piece and was a nuisance in both boxes. Calm on the ball, tracked runs well and didn't give Leicester City striker Jamie Vardy a sniff.
4. Kevin Long 7
Put his heart and soul into his performance at the King Power. Threw himself into everything in and around the box and made some key interventions, particularly in blocking Perez's path in the first half and Vardy's late in the second.