Ryan Sessegnon and Denis Odoi’s goals had the hosts an unpleasant experience by trailing 1-0 from the game at Pride Park.
Before Odoi struck in a header from a corner, teenager Sessegnon fired into the top corner from close range.
Aleksandar Mitrovic and Aboubakar Kamara got opportunities to score more goals, as the Rams created little.
In the final on Saturday, 26th May Slavisa Jokanovic’s side – beaten play-off semi-finalists last season – will play either Aston Villa or Middlesbrough.
Struggling to break down Derby in the first leg, Fulham showed the reason for being unbeaten at home since October displaying fully flowing and attacking the football.
● Relive Fulham’s victory over Derby
During the first half, the Rams frustrated their opponents though Scott Carson superbly saved Mitrovic’s close-range header, and it was not until after the break Fulham made their dominance count.
The Cottagers found out that whom would they face in the final on Tuesday. When Villa took a one-goal advantage over Boro back to the West Midlands.
Fulham finally end play-off hoodoo
Victory in the semi-finals ends a run of seven play-off games without a win for Fulham.
In 2016-17, west London side was defeated by Reading on 2-1 aggregate, but now they are one match from a return to the Premier League for the first time since relegation in 2014.
It will be the first visit for the Whites also to Wembley since 1975 when they were beaten by West Ham in the FA Cup Final.
Fulham finished third in the championship and thirteen points ahead of Derby, only missing out on automatic promotion because of a final day loss at Birmingham. But their performance at Craven Cottage was spectacular since the turn of the year, scoring more goals at home than any other side in 2018.
And they became only the second team out of seventeen in a Championship play-off to lose the opening tie and then go through.
Derby will now spend an eleventh successive season in the second tier despite reaching the play-offs in three of the past five campaigns.
Should England take a gamble on Sessegnon?
In Sessegnon, Fulham consists of one of the most promising young talents in England.
The Championship Player of the Season, who turns eighteen on Friday, has been lauded as an outside contender for a place in Gareth Southgate’s twenty-three- man squad for the World Cup in Russia.
The left-foot winger was kept silent in Friday’s first leg, but this time was instrumental in most things Fulham did in the final third.
He had already seen a shot well saved by Carson before the break when found in space by Kamara but made no mistakes from Stefan Johansen’s chest down just two minutes into the second half.
Fulham’s lead scorer has now netted twenty-two times in eighty career appearances, despite spending most of his first season playing from left-back.
England’s team will be announced on Wednesday.
Reaction – ‘The fans did a crucial job’
Fulham boss Slavisa Jokanovic told BBC London:
“I must be very satisfied personally, for my players and the fans. We made a great step and will bring the team to Wembley after 43 years.
“We believe in our way and the team has shown their confidence. It is a fantastic achievement.”
“We will play the final and know that people only remember the team who wins the game.
“We must enjoy this moment and be happy, especially for our fans as they pushed us all year at home and did a crucial job for us tonight too.”
Derby manager Gary Rowett told BBC Radio Derby:
“The way we performed was the most disappointing thing for us. I think it’s very easy to be critical, but I don’t think that’s the right thing to do.
“I think the players over the two legs have given everything and worked incredibly hard.
“We’ve tried everything, we’ve had a go, we’re disappointed. Sometimes you’ve got to handle that disappointment and move on.
“Three out of the four teams are going to be disappointed at the end of these play-offs and unfortunately we’re the first ones.”