The Fury fell behind when Brazilian midfielder Robson netted for the Gold Coast in just the 9th minute but David Williams grabbed a leveler for the visitors just before the hour-mark to get things back on track.
Young United keeper Jerrad Tyson was being kept busy by the North Queensland attackers but it all got too much when Fury skipper Ufuk Talay put his side ahead with just over 20 minutes remaining.
United were unable to restore parity and were eventually taken to their second consecutive defeat after Friday's loss to Adelaide but they have managed to hold on to third position whilst the Fury remain at the bottom of the table despite their win.
GCU Jerrad Tyson (gk), Steve Pantelidis (Anderson 64'), Robson, Zenon Caravella (Z.Anderson 80'), Bruce Djite, Bas van den Brink, Kristian Rees, Adama Traore, Steve Fitzsimmons (Barisic 52'), Ben Halloran, Josh Brillante
Subs - Scott Higgins (gk), Andrew Barisic (52'), Anderson (64'), Zach Anderson (80')
NQFJustin Pasfield (gk), Jack Hingert (Spagnuolo 62'), Mark Hughes, Ufuk Talay (Tavsancioglu 85'), Gareth Edds, Dyron Daal (Sseppuya 80') David Williams, Panny Nikas, Andre Kilian, Simon Storey, Osama Malik