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Cornet sustained a hamstring strain just before the break, and was withdrawn, before insult was added to injury when Vardy round Nick Pope and slotted into an empty net to make it 2-2.
5. Ben Mee 6.5
Almost punished early on when Vardy squeezed in-between the skipper and Lowton to head over. Couldn't get to Vardy for the equaliser and unable to reach the line in time to deny striker his second. Fought tooth and nail to limit hosts, though, with countless blocks.
6. Dwight McNeil 6
The volume of crosses, that we've become accustomed to, seemed to be lacking. Stayed disciplined in his defensive duties, tracking well, and protected the ball in possession, but quieter than usual in final third. Survived a penalty scare when tripping Castagne.
7. Maxwel Cornet 7.5
Bitter-sweet first Premier League start for the Clarets. Opened his account with a stunning volley and won the corner that led to Vardy's own goal. Got up and down the pitch well, displayed an impressive first touch, but sustained injury before the break.
8. Josh Brownhill 6.5
Competed well, despite being out-numbered in the middle of the park. Lively performance, anticipating when to stick and when to twist, broke up play nicely, calm on the ball, and switched play well to get Burnley moving.