Burnley have one more chance to secure a club record-equalling 11th away win of the season after an unlikely stalemate guaranteed that Leicester will be staying with them in the Championship next season.
Like the Clarets' only previous draw away from home - at Cardiff City a month ago - this also ended goalless.
But how the scoresheet stayed blank remained a mystery as both sides gave everything in pursuit of a winner in a game that produced almost everything bar a goal.
Charlie Austin was twice denied by the woodwork with the same effort as he went closest to adding Eddie Howe's Clarets to the record books and Bunley were denied what looked like a penalty when Sol Bamba blocked a Chris McCann effort with his raised arms.
Leicester also had their hard-luck stories but Burnley's superb rearguard refused to budge, extending their unbeaten run to four games ahead of Saturday's final away trip to the seaside to face a Blackpool side which, like Cardiff, put itself beyond the reach of the Foxes in the top six.
With only maximum points and freak results elsewhere for the remainder of the campaign able to propel either side into the play-offs, it was always likely to be make-or-break stuff at the King Power Stadium and so it proved straight from the start.
Chris McCann's effort is handled by Sol Bamba
The Foxes, unbeaten at home in seven Championship games, came flying out the traps with the lightning quick Lloyd Dyer immediately testing Lee Grant and threatening to give Burnley's back four a testing night.
But having weathered a rapid burst of City's slick passing game, the Clarets produced some top-class football of their own to take the game to the home side.
On a magnificent playing surface Ross Wallace - restored to a more attacking position with Danny Lafferty coming in for his third start in the left-back slot - ran at the Leicester defence at every opportunity and his burst forward and link-up with McCann created a first chance of the night for Austin, who cracked an angled drive at Kasper Schmeichel.
Austin then tried to return the favour for McCann, playing in a more advanced midfield role in place of Danny Ings, from a short back-pass from Bamba when he may have been better going it alone.
And then when the re-called Marvin Bartley and Lafferty combined well, Austin was just unable to make enough of Lafferty's low cross as the Clarets continued to enjoy the space they were allowed in a wide open game.
David Edgar clears from David Nugent
Bamba then made amends for his earlier error with a superb sliding block as Austin looked to pull the trigger again but got lucky when he handled from McCann following an Austin knock-down with even City boss Nigel Pearson admitting afterwards that he feared the worst.
The busy Wallace also tested Schmeichel from long-range but it wasn't all Burnley as Leicester attacked with verve as former Clarets' loanee David Nugent buzzed around in his usual predatory fashion and cracked one effort from fully 35 yards just over the bar.
Grant had to show a strong wrist to beat away a driven free-kick from Ben Marshall and Danny Drinkwater also glanced a header just wide, but remarkably neither side was able to force a break-through before half time.
The status quo almost didn't last for long, though, as twice Leicester went close to going ahead in the opening ten minutes of the second half.
For the second game in a row Kieran Trippier needed to make an instinctive goalline clearance to keep out Lee Peltier's header from a Marshall corner and Grant then made a superb save to deny Nugent after a mistake by Junior Stanislas had played Burnley into trouble.
Charlie Austin is so close to the winner........
.......as the ball hits both posts
........and Sol Bamba then clears
But if that was a close call then City survived an even greater scare as Austin went within a whisker of putting Burnley in front.
The in-form striker met a Trippier cross with a glancing header which beat Schmeichel but bounced from one post to another across the goalline before Bamba arrived from nowhere to clear as Austin moved to tap in what would have been his 49th league goal in his 100th appearance.
Back came the Foxes with Nugent driving them forward and firing at Grant but Burnley hadn't given up hope of taking maximum points either and with McCann unable to shake off a knock, Howe sent on Ings for the final 11 minutes.
Much of his best work was done helping out a defence which finally resorted to soaking up the pressure but in injury time Austin nearly won it when he met another Trippier cross with a header which flew over the bar.
Leicester City: Leicester City: Schmeichel, Peltier, Konchesky, Bamba, Morgan, Dyer (Gallagher 72), Drinkwater, Wellens, Beckford (Schlupp 72), Marshall, Nugent. Subs: Howard, King, St Ledger.
Burnley: Grant, Trippier, Lafferty, Duff, Edgar, Marney (Ings 79), McMann, Bartley, Stanislas (McQuoid 68), Austin, Wallace. Subs: Howieson, Jackson, Jensen.
Booked: Marney 84
Referee: Michael Jones
Attendance: 19,806 (Burnley 294)