Elias Kachunga gave the Terriers an early lead from close range, their first away goal since Matchweek 1, before Aaron Mooy extended their lead.
Watford captain Troy Deeney was shown a straight red card just after the half-hour and Laurent Depoitre extended the visitors' lead after half-time.
Jonathan Hogg became the second man sent off when shown a second yellow card, and Abdoulaye Doucoure capitalised by finding the bottom corner with a spectacular strike.
Mooy scored Huddersfield's fourth with a late penalty after Doucoure had fouled Depoitre.
Huddersfield move up to 11th with 21 points, while Watford remain ninth.
Watford: 23 Dec v Brighton (A)
Huddersfield: 23 Dec v Southampton (A)