Leeds threatened from the outset and the Whites finally went ahead in the 58th minute as Georginio Rutter tapped home from close range after a brilliant Sam Byram header from a Dan James corner had been saved.
More chances then came United’s way but Daniel Farke’s side were then saved by an outstanding save from keeper Illan Meslier to keep out a Kiernan Dewsbury-Hall header with 95 minutes on the clock.
Leicester could have gone 17 points clear of third-placed Leeds with a victory but the Whites instead cut the gap to 11 points as they also moved to within six points of second-placed Ipswich Town in the automatic promotion spots.
Fine pressing from the start led to a golden Whites chance in just the third minute but Joel Piroe could only fire high and wide from just inside the box following Georginio Rutter's square ball.
More rapid pressing as Leicester looked to play out then got Rutter into the box but the forward was tackled as he looked to get his shot away.
At the other end, a brilliant defensive header from Dan James at the far post cleared a dangerous cross with Stephy Mavididi lurking from Leicester's first attack in the ninth minute.
Leeds threatened again eight minutes later as the flying Crysencio Summerville burst into the box but the winger was crowded out before passing to Rutter whose weak shot was saved.
Moments later, Leeds saw claims for a penalty dismissed as Rutter was brought down in a sandwich between Wout Faes and Cesare Casadei who looked to have clipped his heel.
But a good Leicester chance went begging in the 24th minute as a flicked header from Jamie Vardy fell to Casadei who was let down by poor control in the six yard box.
Having already committed a foul moments earlier, Sam Byram was then booked for clattering into Abdul Fatawu as Leicester began to get on top, the Foxes seeing a dangerous cutback from Mavididi deflect off Joe Rodon back to Illan Meslier.
Leeds were then saved by the frame of the goal 11 minutes before the interval as a superb curling effort from Fatawu crashed back off the crossbar after the Foxes star had skinned Byram cutting in from the right flank.
The Whites immediately countered and Summerville was played in before ending up on the deck, boss Daniel Farke fuming that his side were not awarded a penalty.
Summerville had gone past Ricardo Pereira who made the slightest contact with the winger and Farke was booked soon after as play was allowed to continue.
As an end to end first half neared the interval, Fatawu blasted a wild effort over the bar from the edge of the box and the same player then lost his footing when well placed from a Mavididi cross.
The last effort of the half then came from Leeds through Ethan Ampadu who fizzed a shot well wide from the edge of the box as the two sides entered the interval goalless.
There were no changes during the break, after which Leeds wasted a good opening in the 50th minute as a fine Rutter pass played in Summerville who was unable to get the ball out of his feet which allowed Pereira to clear.
Three minutes later, Leeds worked the ball to Piroe whose strike from just inside the box was parried away by Foxes keeper Mads Hermansen who then easily stopped a weak Rutter shot.
A crucial tackle from James Justin then thwarted Rutter as he prepared to pull the trigger in the middle of the box following a Summerville run and pass.
But Leeds were continually threatening and the Whites finally went ahead just before the mark through Rutter following a brilliant Byram header from a James corner.
Byram met the corner with a bullet header which was brilliantly saved by Hermansen but the keeper could only push the ball out to Rutter who could not miss from close range and tapped home to send the away end wild.
Leicester looked to respond and brilliant defending by Rodon and the onrushing Illan Meslier thwarted Mavididi close to the goal in the 70th minute.
From a Mavididi cross, Fatawu then blazed a volleyed attempt from inside the box over the bar but Leeds were a menace on the counter and broke clear from a Foxes corner through James who cut inside but saw his low shot saved.
Leeds were then back under the cosh and a brilliant header from Rodon cleared a dangerous cross for a corner which the Whites survived.
Farke then made a double change with six minutes left as Rutter and Piroe were replaced by Patrick Bamford and Ilia Gruev but Leicester went close again in the 86th minute through Kelechi Iheanacho whose shot from the edge of the box was deflected over the via a big block from Rodon.
Summerville and Leicester sub Hamza Choudhury were then both booked after a clash, after which Summerville was replaced by Willy Gnonto for Farke's third change as the clock hit 90 minutes.
Leicester were then given six added minutes to find an equaliser but three minutes of those passed without incident, after which Farke made another double change in withdrawing Archie Gray and James for Luke Ayling and Jaidon Anthony.
But Leeds were then saved by an outstanding Meslier save to claw a header from Kiernan Dewsbury-Hall out from under the bar with 95 minutes on the clock.
The Foxes were then presented with one last free-kick but an awful delivery from James Justin sailed out of play as the Whites recorded a very impressive success.
Leicester City: Hermansen; Ricardo, Faes, Vestergaard, Justin; Winks, Casadei (Choudhury 67), Dewsbury-Hall; Fatawu, Vardy (Iheanacho 59), Mavididi. Subs not used: Stolarczyk, Coady, Souttar, Albrighton, McAteer, Marcal, Daka.
Leeds United: Meslier; Gray (Ayling 90), Rodon, Struijk, Byram; Ampadu, Kamara; Summerville (Gnonto 90), James (Anthony 90); Piroe (Gruev 84), Rutter (Bamford 84). Subs not used: Darlow, Firpo, Cooper, Poveda, Gnonto