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Inspired by full-back Sam Tomkins, Wigan eased to a 22-0 lead at half-time through tries from Dan Sarginson, Tomkins and two from Josh Charnley.
Luke Gale and Ben Crooks crossed for Tigers in the second half, either side of Dom Manfredi's controversial score.
Wigan remain on course for a record 20th Challenge Cup and will face Super League leaders Hull in the last four.
Saturday's draw also pitted Warrington Wolves against Wakefield Trinity Wildcats, with the ties to be played on 29-30 July.
Castleford had won their previous three Challenge Cup visits to Wigan, last losing in the cup at Wigan in 1948.
Tigers had edged the territory in the first half but Warriors repeatedly broke decisively to take a commanding lead.
The visitors had hope when Gale crossed but any faint hopes of a comeback were dashed when Manfredi's try was awarded.
The on-field official initially ruled that Manfredi had touched down, when racing onto a through kick that was poorly dealt with by Tigers.
The video referee assessed multiple replays but did not find sufficient evidence to overturn the original decision.
The officials needed technology to assess Crooks' late consolation for Castleford too, but correctly judged that he had touched down before going out of play.
Wigan: S Tomkins; Charnley, Sarginson, Gildart, Manfredi; Williams, Smith; Mossop, Powell, Flower, Sutton, Isa, O'Loughlin.
Replacements: J Tomkins, Tautai, Burke, Bretherton.
Castleford: Dorn; Monaghan, Crooks, Minikin, Solomona; Millington, Gale; Jewitt, McShane, Patrick, Moors, McMeeken, Massey.
Replacements: Milner, Tickle, Holmes, Cook.
Referee: Chris Campbell
Wigan Warriors reached the Challenge Cup semi-finals after a clinical first-half display against Castleford Tigers.