The hosts then had captain Troy Deeney sent-off for a reckless lunge on Collin Quaner before the Terriers added a third early in the second-half.
Town then had their own skipper Jonathan Hogg dismissed for two bookable offences before Watford's Abdoulaye Doucoure pulled a goal back with a superb 25-yard half-volley.
However, it proved to be merely a consolation as Mooy converted a penalty in stoppage time after Doucoure fouled Laurent Depoitre in the area.
Have a look below at the quick-fire highlights from this afternoon's game at Vicarage Road.
6 Minutes: GOAL - Elias Kachunga taps in from close range after Watford stopper Heurelho Gomes initially denies Collin Quaner in the area.
8 Minutes: Andre Carrillo brings down Rajiv van La Parra 30 yards out - Aaron Mooy whips the free-kick into the box but but the referee blows for a foul and a Watford free-kick.
14 Minutes: Van La Parra does well to win a corner; Mooy’s delivery falls to Chris Lowe on the edge of the area who's volley is charged down before it falls to the feet of Mathias Zanka but he is ruled offside...
23 Minutes: GOAL - Zanka finds Quaner down the line who whips a beautiful ball across the face of goal which bounces off Mooy’s chest and goes in.
34 Minutes: RED CARD - Troy Deeney is sent-off for a wild lunge on Collin Quaner.
47 Minutes: Quaner bursts past Christian Kabasele into the area; he tries to cut the ball back to Ince but a defender gets across just in time.
50 Minutes: GOAL - Depoitre drills a fierce effort past Gomes from a narrow angle inside the area.
62 Minutes: RED CARD - Second dismissal of the afternoon sees Hogg sent off for a foul on Richarlison and already on a booking he had to go!
68 Minutes: GOAL - Abdoulaye Doucoure drills a superb effort past Lossl from 20 yards out after an initial free-kick was headed clear...Now 3-1.
89 Minutes: Town have a penalty as Depoitre is brought down in the area by Watford defender Doucoure!
90 Minutes: GOAL - Mooy steps-up and makes no mistake about it to grab his second of the afternoon and Town’s fourth!
90+2 Minutes: Quaner is denied by Doucoure on the line after Danny Williams’ cross fell to him in the box!
Huddersfield Town (4-2-3-1): Lossl; Schindler, Zanka, Lowe (Malone, 45’), Hadergjonaj; Hogg, Mooy; Van La Parra (Williams, 63’), Quaner, Kachunga (Ince, 18’); Depoitre
Subs Not Used: Coleman, Whitehead, Cranie, Mounié
Sent Off: Hogg
Watford (3-4-2-1): Gomes; Mariappa (Pereyra, 29’), Prödl, Kabasele; Janmaat, Doucouré, Capoue (Gray, 64’), Holebas (Okaka, 83’); Carrillo, Richarlison; Deeney.
Subs Not Used: Karnezis, Wagué, Watson, Sinclair
Booked: Doucoure, Janmaat
Sent off: Deeney
Half Time: Watford 0 Huddersfield Town 2
Next Match: Southampton at St Mary’s Stadium, Premier League, Saturday, December 23rd (kick off 3pm)