The Tigers had won the first leg 3-0 at the iPro Stadium but were beaten 2-0 in the second leg at the KC Stadium through two first-half goals, an early Johnny Russell strike and an Andy Robertson own goal.
Derby pushed for an equaliser but Hull held on to their narrow advantage to reach the final at Wembley against Sheffield Wednesday and keep alive hopes of an immediate return to the Barclays Premier League.
Knowing the odds were stacked against them, Derby began at a high tempo and took the lead on six minutes when Hull failed to deal with a cross to the back post by Cyrus Christie. The ball was headed down by Chris Martin and fellow Scotland international Russell saw his first shot blocked but forced home the rebound from a couple of yards.
Ten minutes later Russell curled a free-kick just wide as Hull continued to soak up pressure and it took 25 minutes for the home side to have a shot when Jake Livermore fired well over.
Ten minutes before the break Derby got their second when a low cross from the left by Andreas Weimann was put into his own goal by former Dundee United defender Robertson from close range.
In a rare Hull attack after the break Scotland winger Robert Snodgrass cut the ball back but Jason Shackell cleared for a throw as no Hull player was there to take the chance, speaking volumes of their preference for defence. It was a risky tactic but one which ultimately paid off.