Burnley-born Jay Rodriguez's late goal secured a 1-0 win and sent Premier League side Fulham tumbling out of the Carling Cup at Turf Moor.
Chris McCann missed a great chance on 77 minutes when he sent a soft header straight at goalkeeper Pascal Zuberbuhler.
But Rodriguez stepped off the bench to score the winner with two minutes remaining thanks to a cool finish. The 19-year-old rounded the goalkeeper following a superb throughball from fellow sub Chris Eagles.
It means Owen Coyle's men move into the fourth-round draw after stretching their unbeaten run to six games.
Andy Johnson and Clint Dempsey proved a handful for the home defence, with the latter trying to chip Brian Jensen on 17 minutes in what was to prove Fulham's best chance.