Chris Martin converted from the spot seconds before the interval to kick-start Derby's resurgence, with goals from Johnny Russell, Jeff Hendrick and a Simon Dawkins double turning the game on its head before the 65-minute mark.
See how the incredible 90 minutes of action unfolded with Sports Mole's live text coverage below.
7 - Chris Martin has scored seven goals in his last seven appearances for Derby. Paradise.— OptaJoe (@OptaJoe) October 28, 2014
22 - Fulham have now scored in their last 22 home ties in the League Cup. Abode.— OptaJoe (@OptaJoe) October 28, 2014
FULHAM SUBSTITUTES: Stafylidis, Eisfled, Parker, David, Burn, Bettinelli, McCormack
DERBY COUNTY SUBSTITUTES: Mitchell, L Naylor, Coutts, Calero, Thomas, Hughes, Ibe
FULHAM STARTING XI: Kiraly, Zverotic, Hutchinson, Arthurworrey, Kavanagh, Hoogland, Hyndman, Williams, Roberts, Ruiz, Dembele
DERBY COUNTY STARTING XI: Roos, Christie, Keogh, Buxton, Forsyth, Mascarell, Hendrick, Bryson, Russell, Dawkins, Martin