Burnley-born Jay Rodriguez put his Championship side into the Carling Cup fourth round after his goal knocked Premier League Fulham out.
Now unbeaten in six, Burnley found themselves on the back foot with Fulham's £10m Andy Johnson threatening.
Both sides had chances yet a strong Fulham could not make their class tell.
And with extra time looming, substitute Rodriguez stepped off the bench to score the winner with two minutes remaining thanks to a cool finish.
Johnson, yet to score since his club record move from Everton, started off in lively fashion and Clarke Carlisle had to be alert to clear two dangerous crosses away.
As Burnley came more into the game Martin Paterson turned and shot over the bar, before Pascal Zuberbuhler saved from Chris McCann.
Fulham came back into it and Clint Dempsey shot wide from Zoltan Gera's pass, before Gera had a snap-shot blocked.
McCann saw another effort slip narrowly past the post before he had a golden chance to win it, peeling away from his marker only to head Stephen Jordan's cross into Zuberbuhler's arms.
But 19-year-old Rodriguez popped up to round the keeper after Chris Eagles' superb through-ball to win it in the dying stages.
Burnley manager Owen Coyle:
"From start to finish we kept the pace and the tempo of the game high. I thought we earned it.
"Now we are in the last 16 who knows what awaits us. Winning games like this gives you confidence."
On teenage goalscorer Jay Rodriguez, he added: "We believe in time he will be a real number nine. Certainly he has not done himself any harm tonight."
Fulham boss Roy Hodgson:
"The Premier League is our priority and some of my players have niggling injuries.
"I am pleased with our team as many players were in for the first time. We looked on for extra time then we conceded so close to the end.
"Burnley looked a good side. I don't know the Championship well enough but I would think they could do well. They are well organised defensively and have players with pace and skill."
Burnley: Jensen, Anderson (Duff 12), Carlisle, Caldwell, Jordan, Alexander, Elliott, Gudjonsson, McCann, Paterson (Rodriguez 85), Blake (Eagles 75).
Subs Not Used: Penny, Kalvenes, Mahon, Van der Schaaf.
Goals: Rodriguez 88.
Fulham: Zuberbuhler, Baird, Stoor, Andreasen, Konchesky, Teymourian, Ki-Hyeon (Milsom 90), Gera (Pantsil 73), Dempsey, Kallio, Johnson (Nevland 72).
Subs Not Used: Stockdale, Leijer, Brown.
Booked: Kallio.
Att: 7,119
Ref: M Jones (Mansfield).
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