The Foxes gave up two stunning late goals to visitors West Ham -- only to salvage a draw with a 94th-minute penalty by José Ulloa.
The Foxes took a 1-0 lead on an 18th minute Jamie Vardy goal, the 22nd of the season for the remarkable striker who has blossomed as at the advanced footballing age of 29.
But Vardy's performance was marred by a sending off in the second half for a second yellow after a perceived dive in the penalty box.
Vardy got tangled up with Angelo Ogbonna in the 56th minute. Television replays showed incidental contact, but not enough to garner the theatrical reaction of the striker according to referee Jon Moss.
Barring an appeal, Vardy will be forced to sit out Leicester's next match against Swansea City.
But even while fielding 10 men, Leicester looked as though they would cling on to their lead until giving up a penalty in the 84th minute after a foul by Wes Morgan on Winston Reid. Andy Carroll secured the draw and just two minutes later Aaron Cresswell made it 2-1 West Ham.
"We will always fight to the death, and that's what we did," said Leicester's Danny Simpson to Sky Sports after the match. "We can't control all the things, but we can fight and work hard."
"I'm so happy for the team, because we don't deserve to lose the game," added Ulloa.
West Ham were unlucky not to score in the second minute off a Cheikhou Kouyaté header which was barely deflected onto the inside post by Kasper Schmeichel before ricocheting onto the outside post and into the goalkeepers arms.
The play set the tone for what began as a frustrating day for the Hammers -- still in contention for a Champions League slot next season -- and a fateful day for Leicester.
Leicester now need eight points out of their final four matches to keep matters in their own hands.
Two of the matches will be played at their home ground, the King Power Stadium, against Swansea and Everton, while their two away games feature Manchester United, and, eventually, Chelsea in the last fixture of the season.
Leicester stand eight points ahead of second place Spurs, who have a game in hand with a match against Stoke on Monday.
"Blood, heart, and soul," said Leicester's manager Claudio Ranieri after the match, while not contesting Vardy's sending off. "We were magnificent."
West Ham, meanwhile, hold their ground in sixth place, with UEFA competition next year a very realistic scenario -- and Champions League an ambitious dream.
Leicester City is in the process of making one of the most dramatic turnarounds in the history of modern football, considering crippling debts forced the club into administration in 2002.
By 2008, the Foxes had dropped all the way down to the third tier of English football. Two years later, Thai duty free magnate Vichai Srivaddhanaprabha took over as chairman, spurring Leicester's improbable climb back to the top.
Their title chances were boosted again later Sunday as Arsenal dropped a point at home to lowly Crystal Palace to miss another chance to close the gap at the top.
Alexis Sanchez headed the Gunners in front just before halftime at the Emirates, but Arsene Wenger's men were stunned by a late equalizer from Yannick Bolasie.
A second straight EPL draw left Arsenal in fourth spot, 13 points adrift of Leicester with a game in hand, and now looking over their shoulders at Manchester United in fifth place.
Sunday's other game saw Liverpool continue on a fine run, winning 2-1 at Bournemouth thanks to first half goals from Roberto Firmino and Daniel Sturridge.