Two records remained intact as Burnley surrendered a lead to pass up the opportunity of ending Leicester's winning home start.
Dean Marney did his best to make up for the absence of injured top scorer Charlie Austin with a fantastic early goal to set up the possibility of a first away win for the Clarets.
But two goals in 11 minutes at the start of the second half from David Nugent and Jamie Vardy left Eddie Howe's men waiting for their first point on the road as substitute Sam Vokes was twice denied at the death.
The Clarets looked to have been dealt a tough hand when Austin was ruled out with a hip injury to reduce their potential goal threat.
And with Michael Duff also on the injured list, Howe was forced into a defensive change with David Edgar regaining his central berth alongside Jason Shackell.
The Burnley back four was asked some early questions as Leicester popped the ball around in an upbeat start but their threat was largely restriced to long range as Ben Marshall dragged a shot wide and Anthony Knockaert tested the handling of Lee Grant.
And from their first meaningful attack the Clarets showed that they could pack a punch without Austin as they went in front in stunning style.
Responding to the challenge of leading the line as the focal point of the Clarets' attack, Martin Paterson spun perfectly away from Sean St Ledger to run onto a Kieran Trippier pass.
And when Paterson intelligently pulled the ball back, Marney timed his burst forward from midfield to meet the pass first time with a vicious curling drive from the edge of the box that flew into the top corner and literally lifted the net off its riggings.
It was a strike of rare quality as Marney ended a 19-month wait for a Championship goal and gave the Clarets the platform to claim a degree of control thanks to a patient passing game helped by the presence of Brian Stock in a midfield holding role on his first League start for the club.
Having conceded at home for the first time this season in the Championship, Leicester looked to respond against the backdrop of an edgy crowd.
But they were given little encouragement by a Burnley side which defended with growing authority and looked to counter on the break, Joseph Mills and Marney forcing Kasper Schmeichel into saves.
At the other end Grant stopped another long-range drive from Marshall but the Clarets' keeper wasn't overly worried until five minutes before the break when former Burnley loanee Nugent - the Foxes' brightest spark - curled a shot against the top of the bar as City went the closest yet to levelling.
That effort did little to appease the home supporters who showed their frustration at half time but within two minutes of the re-start they were on their feet as Nugent did make it 1-1.
The striker had gone 11 games without a goal but having previously scored five times against the Clarets he couldn't have hand-picked the opposition better to end his drought as he bounced home a scuffed volley for his 100th career goal after the ball was allowed to drop in the box following a long throw.
The goal instantly changed the complexion of the game as City moved up a gear and Burnley struggled to stem the tide.
Grant saved well from Vardy but with 56 minutes gone the former Fleetwood man claimed his third goal of the season to put the Foxes in front, his shot taking a big deflection off Shackell to loop past a wrong-footed Grant and under the bar.
Howe responded with a change in personnel and formation as Ben Mee and Vokes came on and with Junior Stanislas and Cameron Stewart asked to tuck in and support Vokes, both put efforts just wide.
Inevitably as Burnley committed men forward there would be gaps at the back and Stewart did well to track back and combine with Grant to deny Danny Drinkwater after he had been released on the break by Nugent.
When Grant then made a fantastic save to keep out a fierce drive from Knockaert there were still ten minutes for the Clarets to try and rescue a point.
And with just five of those gone they almost did it as Wes Morgan's mis-cued header gave Vokes a chance which the big striker, who had given his side renewed impetus, steered against the foot of a post as the King Power Stadium held its collective breath.
But if that was a let-off for the home side there was a bigger one to come as Vokes, played in by Marney, couldn't beat Schmeichel in the final minute as the big Dane rushed out to smother his shot and finally secure the points as the rebound flew out and off the shins of the waiting Shackell.
Burnley: Grant, Trippier, Mills (Wallace 75), Edgar, Shackell, Stock (Mee 62), Marney, McCann, Paterson (Vokes 62), Stanislas, Stewart. Subs: Bartley, Hewitt, O'Neill, Jensen.
Booked: Paterson 26
Leicester: Schmeichel, St Ledger, De Laet, Konchesky, Drinkwater, Morgan, James, Marshall (Waghorn 75), Vardy (Dyer 75), Nugent (Futacs 89), Knockaert. Subs: Whitbread, Danns, Logan, Beckford.
Booked: Nugent 38, Knockaert 73
Referee: Dean Whitestone