The Clarets suffered a kick in the teeth when Jamie Vardy equalised with five minutes remaining to draw the Foxes level.
The visitors thought they'd stolen the points in the final minute of time added on when Chris Wood headed in off the post once substitute Ashley Barnes had helped the ball on.
The players wheeled away in celebration towards the travelling fans, but ecstasy turned to agony following VAR's intervention.
City substitute Timothy Castagne appeared to have stepped up at the perfect moment, from the home side's point of view, leaving Wood fractionally offside.
It was a cruel conclusion for the Clarets, who had led Brendan Rodgers' FA Cup winners on two occasions.
A Vardy own goal and Maxwel Cornet's first for the club, either side of the ex-England international's equaliser, had given Burnley the lead at the break.
Cornet sustained a hamstring strain just before the break, and was withdrawn, before insult was added to injury when Vardy round Nick Pope and slotted into an empty net to make it 2-2.
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