Shinji Okazaki sent the visitors into a 28th-minute lead, but just five minutes later, Riyad Mahrez was denied by Mark Bunn from the penalty spot and that miss proved crucial as Rudy Gestede equalised for Villa 15 minutes from time.
Claudio Ranieri's side have risen to the summit ahead of Manchester City, but Arsenal would reclaim that spot with a point or better at Stoke City tomorrow. Villa, meanwhile, remain bottom and now nine points from safety.
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The Villa supporters, buoyed by their team's win over Crystal Palace last time out, were extremely vocal in the opening 10 minutes at Villa Park and it was the hosts that enjoyed the majority of the possession early on.
Villa had an excellent chance to take the lead in the 20th minute when a mistake from Robert Huth allowed Libor Kozak to go one-on-one with Kasper Schmeichel, but the Danish international was on hand to make a smart save.
It was the visitors that took the lead moments before the 30-minute mark, however, with Okazaki firing home from close range after Bunn had kept out a lobbed effort from Vardy.
Leicester had a wonderful chance to score a second in the 33rd minute when Mahrez's strike from inside the box was blocked by the hand of Aly Cissokho, which handed the Foxes a penalty. Mahrez stepped up to take it, but the midfielder's poor spot kick was saved by Bunn.
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Villa's best chance of a leveller late in the first period came to Idrissa Gueye, but the 26-year-old's effort was always rising over the crossbar from inside the box.
The home side had the first real chance of the second half, but Schmeichel was equal to a strike from Cissokho, who had driven towards the box after a smart flick from Carles Gil. Danny Drinkwater was next to come close for Leicester just before the hour, but his curling strike from distance was saved by Bunn.
Villa had a strong shout for a penalty in the 61st minute when Huth threw his arm into the face of Kozak, but referee Roger East was not interested, much to the frustration of the home supporters. Leandro Bacuna then came close with an effort from distance, but once again, Schmeichel made the stop.
Leicester had an opportunity on the counter when Vardy rounded Bunn before setting up Drinkwater, but the former Manchester United midfielder could only turn wide of the post.
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Villa had their equaliser in the 75th minute, however, when Gestede's deflected effort found a route past Schmeichel. Kozak had a wonderful chance to win it for the home side late on, but the tall striker could only lift his effort over the crossbar from close range.
Remi Garde's side launched an aerial bombardment in the five minutes of additional time, with crosses into Gestede and Kozak their best avenue. Leicester held out, however, to gain the point they needed to return to the top.
Villa have still only won twice in the Premier League this season, while Leicester have lost just twice, which leaves the Foxes nine points clear of fifth-placed West Ham United.