The Cottagers went into tonight's semi-final second leg looking to overturn a one-goal deficit following their defeat in Friday's first leg, and top-scorer Ryan Sessegnon got them back on level terms early in the first half.
The decisive goal came from a more unlikely source, though, Denis Odoi producing a stunning header to complete the turnaround as Fulham booked a Wembley showdown against either Aston Villa or Middlesbrough in football's richest match on May 26.
Slavisa Jokanovic's side managed only two shots on target throughout the first leg, but it took just two minutes for them to test Scott Carson for the first time this evening when Tom Cairney's long-range strike was gathered by the Derby goalkeeper.
The first clear chance of the contest also went the way of the home side when a quick counter-attack saw the returning Aboubakar Kamara pick out Sessegnon, but the ball got caught underneath the 17-year-old's feet and his eventual effort was well saved by Carson.
Derby were holding their own in open play during a hard-fought contest, but the better sights of goals continued to fall the way of Fulham, and Aleksandar Mitrovic had his first chance in the 20th minute when his tame effort rolled into the arms of Carson after a one-two with Sessegnon.
Mitrovic turned provider five minutes later when he teed up Stefan Johansen on the edge of the box, only for the midfielder to slice his effort off target.
It continued to be Fulham that created the better opportunities despite Derby also carrying a threat when coming forward, and Mitrovic again came close shortly before the half-hour mark when he glanced a header wide of the target.
A good break from Andreas Weimann resulted in Bradley Johnson steering an effort past the post for Derby shortly afterwards, but Fulham were soon back on the front foot with Mitrovic firing another shot wide from range.
The Newcastle United loanee's threat was growing, though, and he came closer still moments later, turning Curtis Davies smartly on the edge of the box before flashing a shot inches wide with Carson beaten.
The Derby keeper kept his side level in the closing stages of the half, first denying Kamara's powerful and dipping effort before producing a stunning reaction save to deny Mitrovic's header from point-blank range, although the Fulham striker will feel that he should not have given Carson the chance to keep it out.
Derby had their own sight of goal in between those two openings in an end-to-end first-half finale, but Cameron Jerome - scorer of the only goal of the first leg - put his long-range shot high and wide.
The Rams failed to have a single shot on target in the first half compared to six for Fulham, though, and the hosts finally took advantage of one of their chances within two minutes of the restart.
Matt Targett's cross was chested down by Johansen for Sessegnon, who took his time despite three Derby defenders closing him down, controlling the ball before lashing his finish past Carson and into the roof of the net to level things up on aggregate.
Derby responded well to going behind with Ikechi Anya nodding an awkward half-chance wide, before they finally registered their first shot on target in the 56th minute when Johnson shrugged off the challenge of Odoi before drawing a save from Marcus Bettinelli from a tight angle.
Mitrovic was a danger all night, though, and the Fulham striker came close again on the hour mark with another smart turn before feeding his shot narrowly past the far post.
Kamara then blasted an effort into the side-netting which took a deflection on its way through, and Fulham got their second goal from the resulting corner when Odoi produced a perfect glancing header into the top corner, leaving Carson rooted to the spot.
Derby boss Gary Rowett immediately turned to his bench for a response, and one of his changes almost made a quick impact when Kasey Palmer picked out an unmarked Weimann, who should have done better with a header which flew well over the crossbar.
The second goal unsurprisingly increased Derby's urgency significantly, but it was Fulham who continued to look the most likely to score in the closing stages, with Carson twice denying Johansen in quick succession as the hosts refused to sit back on their lead.
Derby did have one final chance to force extra time in six minutes of stoppage time when Palmer fed the ball into the path of Matej Vydra, but the Rams' top-scorer - who was left out of the starting lineup - could only fire his effort wide of the target as Fulham held out for their first ever victory in the playoffs.
The Cottagers are bidding to become the first second-tier team to win the playoffs after losing the first leg of the semi-final since Bolton Wanderers in 1995, and they will discover the identity of their opponents when Aston Villa host Middlesbrough with a 1-0 lead on Tuesday night.
FULHAM (4-3-3): Bettinelli; Fredericks, Odoi, Ream, Targett (Kalas 76'); Cairney (Norwood 91'), McDonald, Johansen; Kamara, Mitrovic, Sessegnon
DERBY (3-4-3): Carson; Keogh, Davies, Forsyth; Wisdom, Huddlestone, Johnson, Anya (Vydra 67'); Lawrence (Palmer 67'), Jerome (Nugent 75')