Although Leicester went top, a point ahead of Manchester City and Arsenal, the London club can return to the summit on Sunday by drawing at Stoke.
Shinji Okazaki put Leicester in front in the 28th minute but Villa goalkeeper Mark Bunn saved Riyad Mahrez's first-half penalty, and the Foxes were made to pay when Rudy Gestede rescued a point for the hosts with 15 minutes to go.
"We had the chance to close the match but we missed the penalty and Aston Villa was regenerated," Leicester manager Claudio Ranieri said. "The second half was a big battle and we were unlucky to concede because the striker touched the ball with his hands and the referee didn't see it.
"It was a pity because we were in control. Of course, they tried to push but there was no clear action from them, and we missed two chances on the counter."
The draw left battling Villa nine points from safety but manager Remi Garde can at least highlight improved performances in what seems like a futile struggle against the drop.
"We deserve better than a point," Gestede said. "They had one good chance, and we a few. We are a bit disappointed - we know we have to win games now, but we take the one point. It's still OK.
"It keeps the momentum going. We have to keep this confidence. It will be tough but we have no choice but to fight."
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