Ross Wallace's deflected shot, Chris Iwelumo's 100th career goal and a penalty from Graham Alexander ensured the Clarets followed up their opening-day victory over much-fancied Nottingham Forest, and a draw at Ipswich last time out, with another impressive victory on Saturday.
Goalkeeper Brian Jensen came to the home side's rescue inside the opening minute when he beat away Danny N'Guessan's shot after the Foxes winger had tricked his way into the box.
Burnley thought they had forged ahead in the fifth minute, but Andre Bikey's thumping header, which found the corner of Chris Weale's net, was chalked off by referee Geoff Eltringham, who ruled Clark Carlisle had a fist full of Joao Moreno's shirt in the build-up.
The Clarets began to impose their passing game on the Foxes and had Martin Paterson got his head to Wallace's dangerous looking free-kick, the deadlock could have been broken.
But Leicester were not without chances of their own and DJ Campbell fizzed the best of those just over after Moreno's long ball bounced kindly.
Wade Elliott then tried his luck with a skidding, first-time drive from 20 yards after Iwelumo's knock-down, but Weale, despite an initial stumble, saved well.
A shoulder injury forced Weale's withdrawal and his replacement in goal - Conrad Logan - was beaten within just a few minutes of his arrival.
The substitute keeper's first job was to pick the ball out of the back of the net in the 47th minute, Wallace claiming his first goal for the Clarets since his summer switch from Preston.
The Scottish winger, who embarked on a jinking run and unleashed a stinging left-footed shot, stood and watched as it took a huge deflection off Moreno and crept into the bottom left-hand corner of the wrong-footed Logan's net.
Leicester came out fighting after the break and were immediately on the front foot, forcing a series of corners - but to no avail.
Iwelumo then failed to hit the target with a header from close range after Paterson showed good persistence down the right.
But he soon made amends, the former Wolves forward nodding home his second goal in as many games with 62 minutes gone.
Wade Elliott and Wallace did all the engineering, the latter drove for the by-line and dinked a hanging cross over the stranded Logan, where Iwelumo was on hand to nudge the ball over the line.
Evergreen midfielder Alexander then got in on the act with a trademark penalty in the 73rd minute after Chris Eagles was felled by substitute Michael Lamey inside the box.
Making his 900th club career start, Alexander was not to be denied, side-footing the resulting penalty beyond Logan to assure victory for the Clarets.