History is on the Foxes side as five of the last six teams to top the table on December 25 went on to become champions - Liverpool the only exception in 2013-14.
Riyad Mahrez, whose goal on Monday proved decisive in the 2-1 win over Chelsea, capped a brilliant week with a penalty in each half with Shinji Okazaki ensuring substitute Kevin Mirallas' 89th-minute strike was academic.
Striker Romelu Lukaku won the individual battle of the top flight hot-shots against Jamie Vardy when he scored for the eighth consecutive match - a feat not achieved by an Everton player since Dave Hickson in 1954 - to equalise and move to 13 league goals and within two of his Leicester counterpart.
The Belgium international also has Vardy's Premier League record of scoring in 11 consecutive Premier League matches in his sights, having made it seven in a row in the top flight at Goodison Park, but it was the visitors' proficiency in front of goal which was more impressive.
England boss Roy Hodgson sat next to Amanda Holden in the directors' box but he would not have needed any help in identifying which British (English) talent are in contention for Euro 2016.
While Vardy rarely threatened Tim Howard's goal he won the crucial second penalty and then laid on the assist for Okazaki.
Everton, too, have national team stars in Ross Barkley and John Stones but after a bright start the former was not effective enough in the final third while Stones, alongside Ramiro Funes Mori who was at fault for the first penalty, was exposed by Leicester's clinical approach.
That was typified by the first goal in the 28th minute when Christian Fuchs' throw-in was flicked on by Vardy to Okazaki who did not appear to be offering a serious threat to Everton's goal when Funes Mori brought him down.
Mahrez tucked the spot-kick just inside Howard's right-hand post but within four minutes Lukaku struck his 52nd goal in 102 Everton appearances when Barkley was denied by goalkeeper Kasper Schmeichel and had his follow up blocked on line by Andy King which allowed the Belgian to hammer home the rebound.
In the second half Vardy bent an effort past the far post, the closest he would come to scoring, but had a more direct influence in winning the penalty when he was tripped in the penalty area by Howard as he ran onto Mahrez's through-ball.
Mahrez went to Howard's left this time to register his 10th goal in nine away league matches this season.
Substitute Kevin Mirallas set up a tense finish when he fired home at Schmeichel's near post but Leicester held on, with Leonardo Ulloa forcing Howard to save with his legs in added time.
TWEET OF THE MATCH
Gary Lineker ?(@GaryLineker) - " About to fly to Belfast for @BBCSPOTY
Please hold on Leicester and be 5 points clear as well as top at Christmas."
PLAYER RATINGS
Everton
Tim Howard: 5
Seamus Coleman: 6
John Stones: 6
Ramiro Funes Mori: 6
Leighton Baines: 6
Gareth Barry: 5
Tom Cleverley: 5
Gerard Deulofeu: 5
Ross Barkley: 7
Arouna Kone: 4
Romelu Lukaku: 7
Substitutes:
Kevin Mirallas (on for Kone, 73): 6
Aaron Lennon (on for Deulofeu, 73): 5
Leicester
Kasper Schmeichel: 6
Danny Simpson: 6
Wes Morgan: 7
Marcin Wasilewski: 7
Christian Fuchs: 6
Riyad Mahrez: 7
Andy King: 6
Ngolo Kante: 7
Marc Albrighton: 6
Jamie Vardy: 6
Shinji Okazaki: 6
Substitutes:
Ritchie de Laet (on for Mahrez, 83): 5
Leonard Ulloa (on for Vardy, 87): 5
Nathan Dyer (on for Albrighton, 71): 5
STAR MAN
Riyad Mahrez - His two goals both came from penalties but he also produced a perfectly-weighted pass to help Jamie Vardy win the second spot-kick and offered enough threat down the right to keep Leighton Baines on his toes.
MOMENT OF THE MATCH
Ramiro Funes Mori's foul on Shinji Okazaki to allow Leicester to score the important first goal away from home.
VIEW FROM THE BENCH
Foxes boss Claudio Ranieri got his tactics away from home spot on, content to soak up much of the anticipated pressure from Everton and counter clinically at speed
Roberto Martinez was left to bemoan defensive lapses and another game where possession did not add up to nine tenths of the law.
MOAN OF THE MATCH
Everton's continued inability to turn possession into goals despite having one of the most in-form strikers in the Premier League in Romelu Lukaku.
WHO'S UP NEXT?
Newcastle v Everton (Premier League, Saturday, December 26)
Liverpool v Leicester (Premier League, Saturday, December 26)
Source : PA
Source: PA