Hull tries: Tuimavave (4), Talanoa (8), Fonua (65), Shaul (68)
Goals: Connor (5,9,35,42,52,59,65,68)
Castleford tries: Roberts (27,47), Hardaker (30), Minikin (72)
Goals: Gale (28,31,48,73)
Holders Hull edged closer to a second successive Wembley appearance after beating Castleford 32-24 to book their place in the Ladbrokes Challenge Cup semi-finals, where they will face the 2014 and 2015 winners Leeds.
Castleford's hopes of a league and cup double were ended by a disciplined Hull side who looked to score from every opportunity presented to them at KCOM Stadium.
That meant Jake Connor's kicking was vital and his eight goals went a long way to securing Hull's place in the last four.
Carlos Tuimavave opened the scoring for Hull in the fourth minute with an 85-metre interception try, the 25-year-old stepping in front of Jake Webster to take Ben Roberts' pass and race to the line.
Things got even better for Hull when Fetuli Talanoa powered his way over in Hull's next set. Video referee James Child was called upon to award the score before Connor's right boot made it 12-0 with eight minutes played.
It took Super League leaders Castleford 28 minutes to register their first points of the match.
Just as played looked to have broken down, the ball arrived at the feet of Roberts, who made amends for his role in Tuimavave's try by strolling through a static Hull defence to score under the posts. Luke Gale's conversion made it 12-6 to the hosts.
Connor's restart sailed over the dead ball line to give the resurgent Tigers a penalty on the halfway line and, on their very next set, Castleford drew level.
Gale ghosted into a position on the blind side and taking the Hull defence with him, allowing him to put in a reverse kick for Zac Hardaker to score. Like Hull, Castleford scored on back-to-back possessions and Gale's conversion wiped out their opponents' early 12-point lead.
The Black and Whites quickly responded, though, and Connor's 36th-minute penalty put them back in front 14-12.
It was a slender lead to take into the interval, but Connor extended Hull's advantage to four points three minutes into the second half with another penalty.
Castleford, attacking the end housing their army of supporters, battled back again and drew level with Roberts' second try of the game.
Michael Shenton shifted from left to right before handing off to Roberts to beat two tacklers to score. Gale's third conversion put the Tigers ahead for the first time in the match, leading 18-16.
That lead did not last long, however, with Connor slotting home is third penalty of the afternoon to draw Hull back on terms.
With a place in the last four at stake, every point was precious and when Hull were awarded another penalty three minutes later, arms pointed to the posts for Connor to try again.
However, for the first time in the game, he missed the target and the score remained tied at 18-18.
Castleford's discipline was now a problem. Another kickable penalty was awarded to Hull on the hour mark which Connor converted to put Hull back in front.
The holders were winning even though they had scored fewer tries than their opponents, but they addressed that balance when Mahe Fonua went over in the 65th minute after Mark Minichiello kept the play alive by running 30 metres cross field. Connor's conversion took Hull eight points clear of Castleford at 26-18.
Castleford were shaking and they suffered another blow when Hull scored their fourth try.
It came on Hull's next set when Danny Houghton's break led to Jamie Shaul going over. Connor tagged on two more points to give Hull a 32-18 lead.
Everything seem to centre around Connor, who was just off target with a drop goal attempt moments later.
If Hull thought the tie was over, they were quickly reminded otherwise when Greg Minikin pulled a try back for the visitors and Gale's conversion reduced the deficit to 32-24.
But Hull held on to advance to the last four.
Hull coach Lee Radford: "I'm very proud of my players.
"There were plenty of special efforts and that was needed.
"This is the juicy part of the season, the excitement starts now.
"Leeds will be a tough semi-final. I don't think we've beaten them in nine games so it will be a challenging and tough Yorkshire derby.
"But these are the exciting games to be involved in.
"I thought it would be a tight contest.
"We'd used a lot of interchanges early in the game, so going for goal gave us a bit of a break and refreshed the players.
"The ease in which we got downfield was pleasing.
"We have strong boys and if we can put some shape on that we'll be better.
"I thought we could have played more in second half, but we didn't have shape even though we won the rucks.
"I'm pleased to be in the semis."
Castleford coach Daryl Powell: "Obviously I'm disappointed because it was a poor performance," said Powell, whose side found themselves 12-0 down inside 10 minutes.
"We didn't handle the start well but we battled back well and we thought we could resettle at half-time.
"When we got in front, the way we tried to manage the game was crazy with offloads.
"Hull were too good for us but we have an opportunity against these boys again in the season. They have beaten us twice now this season and we have to find a way to knock them off.
"We have to crack on. This is gone now.
"It's like a play-off game and there are key lessons for us.
"When we have lost this season, we have responded well and we have to bounce back quickly."