In an action-packed first 45 minutes, goals from Caglar Soyuncu and Jamie Vardy turned the game on its head after Dominic Calvert-Lewin had put the Toffees in front, before Jordan Pickford denied James Maddison from increasing the Foxes' lead with a penalty save in first-half stoppage time.
Alex Iwobi then restored parity for Everton less than 10 minutes into the second half, and although four goals were scored on the night, it was a tale of two goalkeepers throughout the contest, with Pickford and Daniel Iversen having nights to remember after making a plethora of crucial saves to force both sides to share the spoils.
A point claimed for Dean Smith's side has seen them move out of the relegation zone on goal difference, now sitting in 16th place and level on points with both Leeds United and Nottingham Forest below them, while Sean Dyche's men sit one point further back in 19th place.
In front of a pumped King Power crowd, both sides made a bright start to proceedings, but it was Everton who began on the front foot, with the first chance inside nine minutes falling to Iwobi, whose sided-footed strike from inside the penalty area was brilliantly tipped over the crossbar by the right glove of Iversen.
The Foxes responded with a decent chance up the other end when Vardy cut the ball back from the left to Maddison in a central area, but he was unable to generate enough power on the shot to test Pickford between the sticks.
Just a minute later, Everton were awarded a penalty when Calvert-Lewin was clumsily pushed in the back by Timothy Castagne, and the Toffees No.9 smashed the resulting spot kick down the middle to put the visitors in front.
The opening goal gave Everton an extra spark in the final third, but that was quickly quashed as Leicester restored parity in the 21st minute courtesy of a first goal since October 2021 for centre-back Soyuncu.
A delivery into the danger zone was eventually headed into the centre by Wout Faes and picked out Soyuncu to slide a volley beyond the outstretched fingertips of Pickford.
Leicester then completed the turnaround in the 32nd minute, with Vardy rolling back the years as he ran through on goal before rounding Pickford and striking into an empty net.
Both sided ended the half strongly an Everton were presented with two great opportunities to level the scores in the final five minutes before the break, with a first-time strike from Dwight McNeil on the edge of the six-yard box saved at point-blank range by Iversen, before the Foxes shot-stopper kept out another close-range effort from Calvert-Lewin.
Just seconds later, Leicester went up the other end with Vardy, who weaved his way around the Everton backline before chipping an effort onto the top of the crossbar.
The first half ended in disappointing fashion for Seamus Coleman as the Everton right-back appeared to sustain a serious leg injury following a tackle from Boubakary Soumare, and the Irishman was replaced by Nathan Patterson after leaving the field on a stretcher.
It looked as if it would go from bad to worse for Dyche's side when Michael Oliver awarded Leicester a penalty kick after Michael Keane stretched his arm out to stop a Harvey Barnes cross into the danger zone.
However, in the ninth minute of first-half stoppage time, Pickford stood his ground to keep out a poor spot kick placed straight down the middle by Maddison to provide a lifeline for the Toffees heading into half time.
That penalty miss proved costly as Everton equalised nine minutes after the break when Iwobi placed a composed first-time volley under Iversen and into the far corner.
Leicester responded well and came close to retaking the lead just before the hour mark when a header from Vardy inside the six-yard was cleared off the line by James Tarkowski.
With the momentum in Leicester's favour, Smith opted to make an attack-minded change, with midfielder Wilfried Ndidi replaced by striker Patson Daka, although Everton continued to pose a threat on the counter-attack
First-half hero Soyuncu almost became a second-half villain when a lapse in concentration almost allowed Calvert-Lewin to reach a cross from McNeil, but Iversen was there to bravely intercept and punch the ball away from danger.
The linesman's flag then came to Pickford's rescue after the Everton goalkeeper lost possession outside his area before Vardy - who has ran into an offside position in the build-up - floated a strike narrowly wide of the near post.
Everton look the more likely to score the decisive fifth goal, but Iversen made another vital save in the final three minutes, expertly tipping a powerful left-footed strike from Abdoulaye Doucoure round the post.
A total of 38 shots were registered in the 90 minutes, with 23 of those for Everton, but neither side were able to find the match-winner and have ultimately come away from the contest somewhat disappointed having created so many chances to win the match.
Leicester and Everton now have a week to prepare for their next Premier League fixtures away against Fulham and Brighton & Hove Albion respectively.