An 86th-minute goal by the defender Matt Elliott ended their relegation worries and left Sheffield Wednesday needing to defeat Liverpool on Sunday and hope others slip up if they are to qualify for Europe.
After a season of winning friends in high places, Leicester feared they might curse the fatal distraction of last month's epic games with Middlesbrough for reaching a state of anxiety of which they had little thought two months ago, when they occupied a lofty ninth place and their membership of the top division was beginning to acquire a look of permanency.
They could trace their worry lines back to the victory over Aston Villa on 5 March that prefaced a run of nine League matches without a win and a yield of only five points that left them still with an unsafe seat going into last night's match.
Happily, the goal by Elliott, the centre-back from Oxford United who could not share their cup glory directly because he was ineligible to play, ensured it did not all end in tears, prompting a typically wry observation from their manager, Martin O'Neill. "It's in keeping with the way we do things to leave it late," he said.
In a tense contest, despite the Sheffield's side leaky defensive form of late - nine goals conceded in their previous two games - it was the home side who looked the more vulnerable, although several attempts by Benito Carbone to beat the redoubtable Kasey Keller from long range were probably not the best approach.
Once Emile Heskey started to leave Richie Humphreys, Wednesday's emergency left-back, in his shadow, Leicester looked much more dangerous. They should have gone ahead after 29 minutes when, following a corner won by Heskey, Garry Parker chipped a short left-to-right cross to the far post only to see Steve Walsh, the Leicester captain, head over the top when it seemed easier to score.
Excitement, as opposed to high tension, was at a premium, the game often in dire need of a spark of originality. Leicester's answer was to take off Parker at half-time, pushing Pontus Kamark into midfield presumably in the hope of providing additional impetus going forward. Sadly, it had no more effect on the character of the contest than the replacement just before half-time of the referee, Gerald Ashby, who had a problem with a calf muscle.
But the breakthrough came when Elliott, at first appearing to be going nowhere as defenders hesitated all around him in the Wednesday penalty area, caught Kevin Pressman by surprise with a shot that crept past the flat-footed goalkeeper almost apologetically.
Leicester City (4-4-2): Keller; Grayson, Elliott, Walsh, Kamark (Prior, 86); Heskey, Parker (Whitlow, h-t), Lennon, Guppy; Claridge (Campbell, 63), Marshall. Substitutes not used: Robins, Poole (gk).
Sheffield Wednesday (4-4-2): Pressman; Nolan, Walker, Stefanovic, Humphreys; Whittingham, Carbone, Atherton, Pembridge; Hirst (Blinker, 80), Booth. Substitutes not used: Nicol, Donaldson, Oakes, Clarke (gk).
Referee: G Ashby (Worcester) replaced by D Crick (Worcester Park) 36.Reuse content