Giants ended Leeds Rhinos’ two-year reign as holders on Friday night and will face a Wakefield side who were given a scare by League One visitors Toulouse Olympique on Sunday, before going through 40-22.
The teams meet at Huddersfield in Super League two weeks before the Cup tie, to be played over the weekend of June 23-26.
Castleford Tigers - who defied an injury crisis to see off Salford on Saturday - will hope history repeats itself after being drawn away to Wigan Warriors, where they won en-route to Wembley in 2014.
Hull’s reward for Sunday’s 47-18 win at St Helens was a home tie against Catalans Dragons, who they beat 28-26 at KC Stadium last weekend.
The full-quarter-final draw, to be played over the weekend of June 23-26, is: Hull v Catalans Dragons, Wigan Warriors v Castleford Tigers, Warrington Wolves v Widnes Vikings, Huddersfield Giants v Wakefield.