A fraught evening saw the Tigers wholly second-best to the Rams, who were as impressive as they were anaemic in the first leg, which saw Hull saunter to a 3-0 win in the East Midlands.
The visitors manufactured two first-half strikes, courtesy of Johnny Russell and an Andy Robertson to make considerable inroads into Hull’s lead as they strove to become the first side ever to turn over a three-goal deficit to make a second-tier play-off final.
But try and they might, Darren Wassall’s side couldn’t restore parity in the tie, with Hull progressing to Wembley on Steve Bruce’s milestone 200th game in charge, although certainly not in the manner he would have wished.
Despite being given a massive scare by the Rams, Hull, somehow held out, despite being second best for virtually the game’s entirely.
Unsurprisingly, Hull fielded the same line-up who secured a pristine 3-0 win at the iPro Stadium on Saturday, with Eldin Jakupovic, as expected, retaining his place in goal in place of back injury victim Allan McGregor.
The only change arrived on the bench where David Meyler replaced Sone Aluko.
Derby made two changes, with Jeff Hendrick and Andi Weimann coming in for ex-Tigers winger Tom Ince and former Leeds midfielder Bradley Johnson.
Derby fans labelled their pre-match task in the East Riding as ‘Istanhull’ in deference to Liverpool’s staggering Champions League final comeback in the Turkish capital against AC Milan almost 11 years ago - when they miraculously came back from three goals down to draw level and force a penalty shoot-out which they promptly won.
The Rams’ task was similarly herculean after a desperate first leg, but they showed similar intent to that showed by the Reds by the Bosphorus in a turbo-charged first period - which yielded an early goal and dominance for the vast majority of proceedings.
Hull, by contrast looked edgy, indecisive and displayed a distinct lack of composure in the poorest of openings, which was seized upon by a jet-paced Derby side quick to expose the hosts’ deficiencies.
Derby, fielding three up front in Weimann, Chris Martin and Russell, with full-backs Marcus Olsson and Cyrus Christie pushing on, went for it from the off.
It yielded fruit on seven minutes with Christie outpacing Snodgrass before delivering a superb cross which was headed across goal by Martin with Russell eventually bundling in on seven minutes.
It was the worst possible start for Hull, with the anxiety palpable in the crowd following a rabbits-in-headlights opening.
Mo Diame just failed to get on the end of Moses Odubajo’s cross in a rare moment of Hull coherence, but other than that, the first half hour was almost exclusively Derby’s, with the hosts looking shaken and sloppy.
Derby looked a yard quicker all over the pitch and needed no second invitation to push players forward with Russell firing a free-kick wide when well placed before Snodgrass was booked for a late challenge on Craig Bryson.
Another dangerous set-piece from a good position on the edge of the box arrived after Livermore fouled Martin, with Hendrick’s effort blocked before the loose ball fell to Bryson, whose rasping shot whistled inches wide as Derby scented a second.
After a tough half-hour, Hull started to belatedly show semblances of life with Livermore seeing a shot deflected not too far wide and Diame dragging an effort off target.
But it proved fleeting with Derby stunning the hosts with a second on 36 minutes.
A break down the left saw Hull stretched with Olsson’s centre turned into his own net by Robertson amid considerable commotion.
The best that Hull could muster before being afforded the welcome sanctuary of half-time was a deflected shot from Moses Odubajo which flew over.
Unfortunately, the second period followed the same vein as the first as Derby should really have drawn level on aggregate with Bryson somehow failing to convert from close-range following Weimann’s cross, with the forward then firing into the side netting.
Another presentable free-kick chance was spurned by Martin after Odubajo tugged at the shirt of the marauding Hughes before Hull were afforded a set-piece chance of their own, which saw Snodgrass’s shot blocked by the defensive wall.
In a bid to inject some badly-needed midfield energy, Bruce made an early change, bringing Meyler on for ex-Rams player Huddlestone, who had an anonymous evening.
The tie was on the proverbial knife edge, with Hull still looking inhibited with the best they could muster seeing Diame fire a low shot off target with Scott Carson having precious little to do in the first hour.
At the back, Hull were once again very much their own worst enemies, inviting pressure on following several panicky clearances.
Michael Dawson then did well to deny substitute Ince before Jakupovic turned away a stinging shot from Martin as dominant Derby pushed for a third to restore parity in the tie.
But Hull, by the seat of their pants, held out with Snodgrass almost soothing nerves with a late strike for the hosts.
Hull City: Jakupovic; Odubajo, Dawson, Davies, Robertson; Elmohamady, Livermore, Huddlestone (Meyler 52), Snodgrass; Diame (Clucas 90), Hernandez. Substitutes unused: Kuciak, Maguire, Bruce, Maloney, Akpom.
Derby County: Carson; Christie, Keogh, Shackell, Olsson (Camara 90); Hendrick, Bryson, Hughes; Russell (Bent 83), Martin, Weimann (Ince 60). Substitutes unused: Grant, Buxton, Bent, Butterfield, Johnson.
Referee: M Oliver (Northumberland).