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  Carlos Tuimavave and Fetuli Talanoa tries and a Jake Connor penalty gave Hull a 14-12 half-time lead, Cas' Ben Roberts and Zak Hardaker replying.
  Connor kicked three more penalties and Roberts crossed again before Hull pulled away when Mahe Fonua and Jamie Shaul scored within two minutes.
  Greg Minikin's late try set up a tense finish but Hull's defence stood strong.
  Hull's victory set up a semi-final with Leeds Rhinos, while Wigan Warriors, winners against rivals Warrington on Saturday, face Salford Red Devils.
  The defeat was only the Tigers' fourth of the season, having won eight successive matches going into the game, with their last loss also coming against Lee Radford's side.
  The hosts had flown into a 12-0 lead early on when Tuimavave intercepted a pass to run nearly the full length of the pitch before Talanoa muscled off two defenders to cross.
  But Roberts showed fleet of foot to find a gap and score, while Hardaker touched down Luke Gale's smart kick.
  Connor's penalty kept Hull in the driving seat, and his kicks kept the score ticking over in the second, as Roberts once more found a gap to get his second try.
  But Hull took a firm grip on the match thanks to two quickfire tries, and although Minikin barrelled his way through down the right, Cas' handling mistakes throughout the match came back to haunt them.
  Hull head 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 game to be involved in."
  Castleford boss Daryl Powell:
  "Obviously I'm disappointed because it was a poor performance. 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."
  Hull FC: Shaul, Michaels, Fonua, Tuimavave, Talanoa, Kelly, Connor, Taylor, Houghton, Watts, Washbrook, Minichiello, Manu.
  Replacements: Bowden, Fash, Thompson, Turgut.
  Castleford: Hardaker, Minikin, Webster, Shenton, Eden, Roberts, Gale, Lynch, McShane, Massey, Sene-Lefao, McMeeken, Milner.
  Replacements: Millington, Patrick, Larroyer, Foster.
  Referee: Phil Bentham
summary: Defending champions Hull FC defeated Super League leaders Castleford Tigers to reach the Challenge Cup semi-finals.