The ex-England striker came off the bench to secure the points for the Foxes after fellow substitute James Maddison had broken the deadlock at Turf Moor.
The 35-year-old netted the seventh goal of his career against the Clarets after Harvey Barnes had put the ball on a plate for the forward in the 90th minute.
The hosts were just minutes away from climbing out of the bottom three, at the expense of Everton, but a double-change from Brendan Rodgers altered things significantly.
Vardy set up Maddison in the 82nd minute and then rounded things off when heading home his first Premier League goal since November.
Burnley goalkeeper Nick Pope had previously done everything he could to keep the visitors out — keeping out Ricardo Pereira, Patson Daka and Harvey Barnes twice — during a display that ought to enter him into the discussion for England selection.
Here are the ratings.
9. Ashley Westwood 5
His first start since recovering from Covid and the midfielder wasn't able to match his usual energy levels in the middle of the park. Slightly laboured in his press and rushed into passes when the ball was played into him. Distribution from open play didn't hit the mark, but he landed a number of corners in dangerous areas, particularly in the second half. Photo: Nathan Stirk
10. Wout Weghorst 6
The Dutchman did his best to make things happen for himself, but the service into him was at a premium at Turf Moor on Tuesday night. Never shies away from a battle for the ball, linked up nicely with his team-mates when given the opportunity, but missed a gilt-edged chance to equalise from a corner late in the day. Photo: Stu Forster
11. Maxwel Cornet 5
Another quiet outing for the Ivorian, who has failed to hit the heights of his performances pre Africa Cup of Nations. Couldn't impose himself on Amartey or Soyuncu, who were both physically superior, and struggled to get in the game. Had a goal ruled out for offside in the first half and should've perhaps done slightly better when played through by McNeil in the second. Photo: Alex Livesey
12. Nathan Collins 6
Failed to cut off Barnes's first half run, which concluded in a magnificent save from Pope. Backed off Maddison on the edge of the box for City's first, failing to engage with the midfielder as he closed in on the edge of the penalty area. Had looked calm and assured in-between. Photo: Lewis Storey