Anthony Elanga opened the scoring shortly after the first whistle, firing into the top corner and a fine team move from the kick-off.
A mistake from Will Fish allowed Derby to equalise through Olamide Ibrahim four minutes later.
Another mistake from the United backline allowed the Rams to take the lead upon the half-four mark, only for Ethan Galbraith to equalise for Neil Wood's side just moments later.
From there, United's plethora of attacking talent took over the game.
After a swift counter-attack started from Hannibal Mejbri ended in a tap-in from Shola Shoretire after the goalkeeper saved a shot from Elanga.
Shoretire turned provider for the next goal, dinking the ball over the defence for debutante Omari Forson, with the 16-year-old firing low between the keeper's legs.
Elanga and Shoretire then both got their second goals of the game, before another debutante, Zidane Iqbal, rounded out the victory for United.
The performance of Forson was a particular highlight for United's youngsters.
Having signed from Tottenham in 2019, the English teenager seems to be yet another attacking gem emerging from the academy set-up.