Brighton went ahead on 28 minutes when Abdoulaye Doucoure diverted Pascal Gross's cross past his own goalkeeper.
Florin Andone converted Davy Propper's cross to double the visitors' advantage 20 minutes into the second half.
Mat Ryan preserved his side's lead with a fine save from Watford's Craig Dawson before substitute Neal Maupay marked his Premier League debut with a goal to secure the Seagulls' victory with 13 minutes to play.
Watford: 17 Aug v Everton (A)
Brighton: 17 Aug v West Ham (H)
Referee: Craig Pawson; Assistants: Ian Hussin, Richard West; Fourth official: Peter Wright; VAR: Andy Madley; Assistant VAR: Mark Scholes