Huddersfield overcame Challenge Cup holders Leeds to reach the last eight for the first time in three years.
Leeds, treble winners last season, seem unlikely to challenge for silverware this term as they sit bottom of the Super League after 13 games.
Tries from Ukuma Ta’ai, Jermaine McGillvary and Ryan Brierley put Giants 19-6 up at the break after Jimmy Keinhorst put Leeds ahead.
Kyle Wood and Danny Brough’s second-half tries ensured the Giants’ win.
Victory for Huddersfield came 12 months after they were beaten by Leeds at the same stage of the competition and a week after they ended a run of five straight derby defeats against the Rhinos with a 28-20 win in the league.
The Challenge Cup also offers Huddersfield their only realistic shot at silverware themselves this term as they sit second from bottom in Super League, equal on points with Leeds.
Keinhorst gave Leeds the ideal start, finishing off fine work from Jordan Lilley to open the scoring inside the fist minute.
Giants responded with three unanswered tries and a drop goal from Jake Connor in a first-half that ended with Rhinos’ former Huddersfield forward Brett Ferres in the sin-bin for dissent after Brierley touched down.
Liam Sutcliff’s effort and a second Keinhorst try gave Leeds hope, only for Woods to go in for Huddersfield and Brough to add another 13 points with two further conversions, a penalty kick, a try and three drop goals of his own.
Anthony Mullally grabbed a fourth Rhinos score with less than six minutes remaining, but it came too late for Leeds to salvage their season.
Huddersfield Giants: Brierley; McGillvary, Cudjoe, Murphy, Connor; Brough, K Wood; Crabtree, Hinchcliffe, Johnson, J Wardle, Ta’ai, Lawrence.
Replacements: Rapira, Mason, Roberts, S Wood.
Leeds Rhinos: Hardaker; Golding, Watkins, Keinhorst, Handley; Sutcliffe, Lilley; Galloway, Burrow, Garbutt, Walters, Ferres, Jones-Buchanan.
Replacements: Mullally, L Briscoe, Cuthbertson, Achurch.
Referee: Ben Thaler (RFL)