The result lifted Watford two places to 18th on eight points from 12 games while Norwich, who last won in September when they upset champions Manchester City 3-2 at Carrow Road, dropped to the foot of the table on seven points.
Watford manager Quique Sanchez Flores acknowledged the early goal was crucial...
Brighton dominated possession but could not find any way through at a windswept Amex Stadium until substitute Trossard poked home Martin Montoya's cross in the 68th minute.
Manchester United manager Ole Gunnar Solskjaer did not agree with VAR's decision to award his side the first of their two penalties in a 3-1 victory over Norwich on Sunday.
United cruised on the day thanks to goals from Scott McTominay, Marcus Rashford and Anthony Martial but could have scored more if not for seeing two efforts from the spot saved by goalkeeper Tim Krul.