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Cornet sustained a hamstring strain just before the break, and was withdrawn, before insult was added to injury when Vardy round Nick Pope and slotted into an empty net to make it 2-2.
Here are the ratings.
9. Ashley Westwood 7
Superb delivery forced Vardy to glance the ball into his own net. Set-pieces that followed went without reward, but were also on the money. Moved the ball accurately and effectively, linking up well with team-mates in and around the penalty area.
10. Matej Vydra 7
Provided the Clarets with an out-ball, getting the better of both Soyuncu and Vestergaard in the foot race. Always posed a threat in behind and produced the cross for Cornet's volley. Visitors didn't play to his strengths after the break.
11. Chris Wood 6
Suffered a real kick in the teeth with what he thought was a late winner against his former club. Competed well in the air, tying up City's centre-halves to open up space for Vydra, but only other sight of goal was fired wide at the near post.
12. Johann Berg Gudmundsson 5.5
Worked diligently with and against the ball after replacing injured Cornet just before the interval. Full of running, rarely conceded possession, kept play alive a number of times, and should have won a free kick in the build up to Leicester's equaliser.