It took them 87 years to taste success there and they are now just 80 minutes from a return appearance after this absorbing quarter-final win.
For all ambitious Castleford Tigers are runaway Super League leaders, Hull made it clear early on that their visitors would need to create something special to usurp them from the famous knockout competition.
However, on a day when they needed to be at their stunning best, Daryl Powell’s side instead produced arguably their worst display of the season as they wilted badly in the heat.
Uncompromising Hull, with Liam Watts and Mark Minichiello leading the way up front and the likes of Carlos Tuimavave and Fetuli Talanoa immense wider out, were far more accurate in everything they did, which was crucial in such stifling conditions.
Unusually, Jake Connor kicked four penalties which pointed at how close his coach Lee Radford thought the game may be, the scrum-half’s fourth successful attempt nudging them back in front 20-18 on the hour as the visitors continued to test the patience of referee Phil Bentham.
It was two tries in three minutes not long after, though, that proved the critical intervention for the East Yorkshire club.
After a handling error from Castleford captain Michael Shenton, Minichiello crabbed across field past tiring defenders to find Mahe Fonua who, outrageously, dummied between his legs before powering over himself.
In the next set, Connor and fit-again Danny Houghton combined to split Castleford on halfway, Jamie Shaul provided the link before Tuimavave stood in the tackle to return the pass for the full-back, who scored the winner at Wembley, to seal this tie in the 68th minute.
Castleford came to life at the end with Greg Minikin’s try giving them hope but Hull’s resilient defence made sure there was no further leakages and so they head into next month’s semi-final and another Yorkshire derby this time against Leeds Rhinos.
Earlier, it looked like being a lot simpler as Hull eased into a 12-0 lead just seven minutes.
Firstly, Tuimavave picked off Roberts’s pass to race 80m just as the visitors looked set to exploit an overlap.
Soon after, powerful winger Talanoa found himself up against Minikin one-on-one and simply proved too strong for the Castleford player who was shrugged away having tried to tackle his opponent around the chest.
Connor improved both scores and Hull were unlucky not to add to their tally when Albert Kelly darted for the line but could not safely get it grounded.
Furthermore, forwards Josh Bowden and Danny Washbrook also both got over the Castleford line but were prevented from touching down by desperate defence.
The visitors, in particular, looked to struggle with their line speed in the soaring temperatures and they will have been glad to see the prearranged water break arrive after 22 minutes.
But Powell’s side were strangely ineffective with the ball; whereas so many things have stuck for them this season, lots of it came unstuck here.
Shenton seemed to have got on the outside of Steve Michaels in good attacking position but lost possession while, when Luke Gale glided through a gap, Greg Eden seemed certain to score his 34th try of the the year.
However, as the winger reached behind him to take his scrum-half’s pass tight to the touchline – as he has done so many times this year – this time he couldn’t reel it in as Hull were let off again.
Later on, even Gale dropped one without anyone near and it was all so out of character.
They did, though, get their act together long enough to score two tries in three minutes to suddenly turn things around.
That said, Benny Roberts’s effort came after hooker Paul McShane was caught in possession on the last tackle and forced to scruffily hack it back to the Kiwi stand-off who then accelerated between Washbrook and Sika Manu.
Their second was far classier; Connor sailed the restart dead gifting Castleford possession, from which Gale darted blind behind a ruck to take possession but then immediately dinked a clever grubber back infield for the onrushing Zak Hardaker to cross.
Gale improved both but his side went in 14-12 down after a harsh decision allowed Connor to kick the first of his four penalties. He added his second early in the second period after a needless swinging arm from Jesse Sene-Lefao but, after Shaul spilled in the tackle coming away from his own line, some brilliant footwork from Roberts saw him glide through for his second try.
Gale’s conversion put his side 18-16 ahead but their ball control and discipline continued to let them down and the Cup holders retaliated mercilessly.
Hull: Shaul; Michaels, Fonua, Tuimavave, Talanoa; Kelly, Connor; Bowden, Houghton, Watts, Washbrook, Minichiello, Manu. Substitutes: Thompson, Taylor, Turgut, Fash.
Castleford Tigers: Hardaker; Minikin, Webster, Shenton, Eden; Roberts, Gale; Lynch, McShane, Massey, Sene-Lefao, McMeeken, Milner. Substitutes: Millington, Patrick, Larroyer, Foster.
Referee: P Bentham (Warrington).