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Leicester's goal-machine Vardy had not found the net since December 21 but converted a penalty just past the hour to double Leicester's lead shortly after replacing Kelechi Iheanacho.
Harvey Barnes had opened the scoring before halftime.
Vardy struck again after 79 minutes to take his league tally to 19 for the season before Barnes claimed his second to make it a miserable night for Leicester's Midlands rivals Villa.
It was the Foxes first win in five league games, ending a slump that had put their top-four place in peril.
Third-placed Leicester began the night only five points above fifth-placed Manchester United but the victory means they have re-established a healthy gap. Leicester have 53 points from 29 games, Chelsea have 48 and United 45.
All have nine games remaining.
Dean Smith's Villa remain second from bottom, two points below the safety line with 25 points and a game in hand.