Young scored his opener with a low shot from Jesse Lingard's pass before curling in a superb free-kick to double the lead.
Anthony Martial struck a third and Watford goalkeeper Heurelho Gomes made a double save to deny Romelu Lukaku and Lingard before Richarlison headed on to the bar.
Watford produced two quickfire goals by Troy Deeney, from the penalty spot, and Abdoulaye Doucoure, from Andre Carrillo's pass.
But a Lingard solo effort sealed the win which puts United five points behind leaders Manchester City.
Watford: 2 Dec v Spurs (H)
Man Utd: 2 Dec v Arsenal (A)