A spectacular late strike from Jordan Cropper lit up Turf Moor and took the Clarets into the fourth round of the FA Youth Cup.
Cropper hammered home a long-range effort from out of the blue that the 17-year-old will remember for a long time.
It was the Clarets’ only effort on target of the night and came six minutes from the end of a tie largely dominated by Leeds.
But it was reward for the Clarets’ perseverance, determined defending and fine goalkeeping from Adam Bruce in a dramatic finish as they knocked out their Roses rivals to go into the last 32 for the third time in four years.
The first half had been pretty much a non-event with Burnley – who included none of the players who had started last Saturday’s league win over Leeds - happy just to reach the break on level terms.
Leeds, coached by ex-Leeds and Scunthorpe defender Mark Jackson, were by far the more composed side as the young Clarets looked to be suffering a case of stage-fright.
But despite dominating possession, particularly in the opening stages, the Yorkshire side failed to make it count.
And after two early chances they didn’t threaten again in a dull first 45 minutes.
Bulgarian youth international and ex-Barcelona junior Dzhoshkun Mihaylov dragged a shot wide and towering centre-back Liam Kitching headed just wide from a corner – both inside the opening 10 minutes.
The Clarets had struggled to get Dwight McNeil – a regular in the under-23s this season – into the game.
But stand-in boss John Townson - deputising for Danny Cadamarteri who was attending a coaching course – made a change at the break, moving Cropper forward into a 4-4-2 formation.
And McNeil (above) immediately had the Clarets’ first chance of the game as he broke clear and sent an angled left-foot shot just wide of the far post.
That wasn’t the start of a spell of pressure from Burnley, though, as Leeds again took charge and after Jamie Shackleton had shot wide, it took an excellent block from Scott Wilson to prevent United skipper Callum Nicell from locating the target.
Jack Clarke then wasted a chance for the visitors at the far post as he failed to convert a low cross before Wilson again blocked, this time from Bobby Kamwa, as Leeds tried to avoid the prospect of extra-time.
The Clarets were doing everything to keep the visitors out but lived dangerously again with 10 minutes to go when Mihaylov forced Bruce into his first real save as he managed to thread a low shot through a wall of Burnley bodies.
And that proved crucial as the Clarets then struck against the run of play to nick the tie with six minutes to go.
Schoolboy Mitch George had livened Burnley up since coming off the bench as an added attacking option, but it was Cropper who grabbed the limelight.
The former Ilkeston Town youngster looked to have little on when he picked the ball up mid-way into the Leeds half.
But after being allowed to stride on, the first-year scholar looked up and from 25 yards buried a shot low into the bottom corner.
Bruce then made a fine save to deny Kamwa and in the last minute of six added on for stoppages superbly kept out a Clarke free-kick as the Clarets doggedly sealed their place in round four.
Burnley: Bruce, Cropper, Clarke, Younger, Wilson, Kershaw, Moss (Meredith 90), Jumeau, Yari (Mpofu ht), McNeil, Barnett (George 73). Substitutes: Calderbank-Park, Major.
Leeds United: Male, Odunston (Wollerton 73), Gotts, McCalmont (Hudson 90), Kitching, Casey, Kamwa, Shackleton, Mihaylov, Nicell, Clarke. Substitutes: Kroma, Lyons, Amissah.
Referee: Daniel Issawi