A day that began with an astonishing game at Carrow Road that finished Norwich City 4-5 Liverpool ended with Leicester three points clear of Arsenal, who host Chelsea today, and Manchester City.
Sergio Aguero scored twice yesterday as Manchester City drew 2-2 at West Ham United, taking them above Arsenal on goal difference, but Manchester United's season took another downward lurch in a 1-0 home defeat by Southampton.
"I don't know if we are a (title) contender at this moment," said Leicester manager Claudio Ranieri.
Vardy rounded Jack Butland to score his 16th goal of the campaign as Leicester sank Stoke at the King Power Stadium, with Danny Drinkwater and Leonardo Ulloa also on target.
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Manchester City were unable to follow suit as they dropped points at West Ham, giving Arsenal a chance to move three points above them.
West Ham took the lead inside a minute at Upton Park as Enner Valencia drilled home after Cheikhou Kouyate's cross was deflected into his path.
Aguero hit the post with an audacious lob from wide on the left before equalising with a ninth-minute penalty after he had been tripped by Carl Jenkinson.
"It was not what we wanted before the game," City manager Manuel Pellegrini told Sky Sports.
"It was a difficult game. I was not happy with the way we conceded the second goal."
Aguero's second goal prevented West Ham from knocking Manchester United out of the top five, but there was little for under-fire United manager Louis van Gaal to cheer after his side were booed off at Old Trafford.
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Charlie Austin gave Southampton victory in the 87th minute, meeting James Ward-Prowse's right-wing free-kick with an unerring header in his first appearance since signing from Queens Park Rangers.
A beaming Austin said: "It does not get any better than that."
In a further blow to Van Gaal, right-back Matteo Darmian was forced off after a second-half collision with Shane Long, exacerbating United's defensive injury crisis.
United are now 10 points below Leicester, five points off the Champions League places and only three points above Liverpool, who saw off Norwich in a dizzying game thanks to a 95th-minute winner from Adam Lallana.
But goals from captain Jordan Henderson and Firmino drew Liverpool level and although Milner's 75th-minute effort was cancelled out by Sebastien Bassong's drive in the 91st minute, Lallana had the final word.
"At the end we can be really happy with nearly everything, especially with the three points," said Liverpool manager Jurgen Klopp, who lost his glasses in the touchline celebrations after Lallana's winner.
"I usually have a second pair of glasses, but I can't find them because it's hard to find glasses without glasses!" he joked.
Palace took a 30th-minute lead when Jan Vertonghen turned Wilfried Zaha's cross into his own net, but Harry Kane equalised in the 63rd minute by heading in Nacer Chadli's cross.
Alli struck in the 84th minute, flicking the ball over a defender's head and brilliantly volleying home from outside the box, before Chadli added a third goal from long range in stoppage time.
Newcastle United remain in the bottom three after losing 2-1 at Watford, who prevailed through goals from Odion Ighalo and Craig Cathcart, with Jamaal Lascelles reducing the arrears.
Elsewhere, bottom club Aston Villa drew 0-0 at West Bromwich Albion.