After a disappointing display in the first leg at Pride Park on Friday, Fulham - beaten by Reading at the same stage last season - were much more of a threat in the return.
Ryan Sessegnon of Fulham.
Sessegnon scored the opener and delivered the corner for Denis Odoi's victor as Fulham overcame a 1-0 first leg deficit and earned themselves a first trip to Wembley in 43 years.
Indeed, he netted against Derby in Fulham's 2-1 win at the iPro Stadium back in March and was an integral part of his side's 23-match unbeaten run that ended on the final day of the season.
Derby have become accustomed to life in the second tier since dropping out of the Premier League in 2008 and the failure to progress to the showpiece final at Wembley on May 26 means the Rams have succeeded in just one of their seven play-off campaigns.
Carson then had to be alert to tip Aboubakar Kamara's effort over the bar before the keeper produced an incredible point-blank save to keep out Mitrovic's close-range header.
Cate Blanchett Just Led a Women's March at Cannes
Its key commitments include the compilation of statistics to record the gender of the filmmakers and key crew of all submissions. The Cannes Film Festival has always been criticized for gender imbalance on its juries and in its film selection.
The boosted price of 23/20 (2.15) on Mitrovic to score in 90 minutes is set to be extremely popular as Fulham aim for a Premier League return after four years away.
The decisive goal came in the 66th minute when Belgian Odoi beat Carson with a brilliantly angled header from a corner.
Fulham will be making it to Wembley for the first time in 43 years, where the face the victor of the game between Aston Villa and Middlesborough. Tonight, we gave everything but it just wasn't quite enough.
Derby boss Gary Rowett felt his team had been too nervous.
"They outplayed us in the second-leg and they more than deserve to go through".