Substitute Nathan Dyer's brave header, seven minutes after Jamie Vardy's 82nd minute equaliser, completed the turnaround to leave Leicester with 11 points from five matches, four behind Manchester City who still boast a 100 percent record.
Leicester are now unbeaten in nine Premier League games stretching back to last season's escape from relegation while shell-shocked Villa languish on four points.
Tottenham Hotspur claimed their first win of the season thanks to Ryan Mason's late winner in a 1-0 win at Sunderland although he was then carried off on a stretcher.
The win lifted Spurs to 12th in the table and dropped champions Chelsea, beaten 3-1 at Everton on Saturday, down to 17th and in danger of falling into the bottom three when Newcastle United play at West Ham United on Monday.
Leicester manager Claudio Ranieri praised his side's spirit after goals from Jack Grealish shortly before halftime and Carles Gil's superb curled finish just past the hour seemed to have put visitors Villa in control.
"It's fantastic, fantastic spirit, good character," former Chelsea manager Ranieri told Sky Sports. "After we went 2-0 down I looked at them and I could see they believed anything was still possible... that's what I love."
Grealish stroked home his first Villa goal when the ball came out to him on the edge of the area.
Leicester pushed Villa back throughout the second half but a lightning counter-attack in the 63rd minute ended with Gil wrapping his left foot around the ball to give Leicester keeper Kasper Schmeichel no chance.
Rather than deflate Leicester, they attacked with renewed vigour and were given a lifeline in the 72nd minute when Ritchie De Laet's flicked volley hit the underside of the bar but was correctly adjudged to have crossed the line.
With Riyad Mahrez causing havoc, Villa were hanging on desperately when the Algerian drove into the area and picked out Vardy who planted his shot past Brad Guzan.
Seven minutes later Mahrez clipped a ball goalwards and the diminutive Dyer stooped to head into the net despite being clattered by Villa's keeper.
Dyer, who needed treatment, was unaware he had scored.
"The physio treating me told me I scored. I didn't know beforehand. It was a nice feeling. I was just dazed -- it was easy to get back up," he said.
Tottenham's match winner Mason was also in the wars.
Mason's 82nd-minute dinked effort, with Erik Lamela splitting the defence after combining with Harry Kane, broke the deadlock at the Stadium of Light.
It was a rare burst of brilliance in an otherwise uninspired encounter but Mason was carried off shortly after following a collision with Sunderland goalkeeper Costel Pantilimon.
Manager Mauricio Pochettino said the player's condition would be assessed on Monday.
"It was a big knock on the knee. It was a great goal and we showed how we try to play," he said.
Sunderland, still searching for their first win after five games this season and now with 11 goals conceded, dropped to the bottom of the table and behind Stoke City on goal difference.
Jack Rodwell might have grabbed a late equaliser but his shot smacked against the crossbar.
"We had the better chances at the start, we knew we were playing against a good side and the speed of the game was unbelievable. Some players could not handle it in the end," Sunderland manager Dick Advocaat said.
(Reporting by Alan Baldwin/Martyn Herman, editing by Pritha Sarkar)
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