The striker put through his own net for the first time in his career but his brace ensured the Foxes grabbed a 2-2 draw.
Maxwel Cornet's goal left Burnley on the brink of their first win at Leicester for 14 years before Vardy struck with five minutes left.
Chris Wood thought he had stolen the points in stoppage time when he headed in but the goal was correctly ruled out by VAR for offside.
The draw kept the battling Clarets, who impressed with their defensive resolve, in the Premier League drop zone while the Foxes sit 12th.
Youri Tielemans drilled over before teeing up Vardy, only for the striker to head over after 10 minutes.
The forward, making his 400th career appearance, should have scored and he marked his milestone in the worst possible fashion by giving Burnley a 12th-minute lead.
Leicester mounted a response and Barnes tested Nick Pope from distance as the hosts dominated the ball.
Burnley held firm, although they needed Lowton to be in the right place to brilliantly block Vardy's close-range effort after Ricardo Pereira was allow to deliver from the right.
The striker would have been forgiven for thinking it was not his day but he came good eight minutes before the break.
Referee Chris Kavanagh played a good advantage after Barnes was clobbered and when Tielemans fed Vardy his first-time effort found the bottom corner.
Yet, just three minutes later, Burnley stunned the Foxes again when Cornet grabbed his first Clarets goal.
The industrious Vydra wriggled free on the right and his deep cross found Cornet to arrow a fine volley past Schmeichel from 12 yards.
But Burnley suffered a blow when the Ivory Coast international was forced to limp off soon after with a hamstring injury – not before being booked for time wasting having come back on the pitch for treatment.
It would have been a relief for the Foxes' defence, again struggling without the influential Jonny Evans, who continues to battle a foot problem.
Leicester, though, failed to rediscover composure after the restart with Schmeichel particularly guilty of poor decision making and battling Burnley remained equal to their threat.
Again, they dominated possession but failed to force Pope into any meaningful save with Iheanacho seeing a shot blocked.
Rodgers' decision to replaced Lookman with James Maddison was met with jeers from the home fans to underline their frustrations.
Tarkowski headed Tielemans' drive behind with seven minutes left and, just as it looked like Burnley would hold on, Vardy struck again.
Iheanacho put him clear on the left and, when Pope raced out, the striker rounded him to roll in the equaliser.
There was still time for more drama in stoppage time when Wood headed in but the goal was ruled out for offside by VAR.