James Wilson fired a second-half winner by capitalising on a rare glimpse of goal and there were stirring showings from a number of individuals to keep another clean sheet, Ben Amos' eighth shut-out in 13 games at this level.
Spurs fielded a strong line-up that included ex-Red Zeki Fryers, Mousa Dembele and Nabil Bentaleb, so it was no surprise they dominated possession. With Joyce's side struggling to get anywhere near Jordan Archer's net, the first half became all about containment with Amos and Charni Ekangamene excelling.
Josh Onomah had the ball in the net in the third minute, although the whistle had long since sounded, and he forced a near-post save out of Amos soon afterwards. A nasty head injury to Guillermo Varela did not help United's cause and saw Saidy Janko switched to right-back while lone striker Wilson did more work in his own box than at the other end.
Souleymane Coulibaly turned Ekangamene and fired well wide but the visitors' Belgian centre-back made an outstanding sliding interception to halt Onomah. Amos took centre stage by thwarting Kenny McEvoy and both Ruben Lameiras and McEvoy with a smart double stop before, when the keeper was beaten by McEvoy's shot, the ball hit the side-netting.
However, there were signs of the Under-21 champions stringing some positive moves together towards the end of the first half and, although the second period followed a similar pattern, Amos was less involved other than to pluck a few crosses out of the air.