It took just six minutes for Huddersfield to draw first blood.
Watford forward Troy Deeney was then sent off before the break for a rash challenge on Collin Quaner.
But despite Abdoulaye Doucoure's 68th-minute stunner, Watford could not complete an unlikely comeback and Mooy added his second from the penalty spot late on to cap a superb day for the visitors. This is the first top-flight meeting between the two sides.
Quaner clashed with Holebas in the Watford box, the ball ran loose to Depoitre and the striker shot home despite Gomes getting a despairing hand to the ball.
Huddersfield Town travel to Watford this weekend to take on the Hornets at Vicarage Road.
And matters soon got worse for the Hornets when captain Deeney saw red having lunged in recklessly from behind on Quaner.
Huddersfield have failed to win any away games since the opening day of the season, and they are now experiencing a goalscoring drought of ten hours while on the road from the John Smith's stadium.
Watford's fight-back was short-lived though and Mooy made no mistake with a spot-kick in the 89th minute after Doucoure clumsily barged into Depoitre in the hosts' area.
David Wagner: "We've had the feeling that this has just been around the corner even if the results have not been there. Our first focus is that we perform at our best and then we will see what we can do". I'm proud and delighted for the players and the away support today was absolutely incredible.
BC-SOC-Watford-Huddersfield, 155 Mooy double as Huddersfield wins 4-1 at WatfordAP Photo LON823, LON820, LON825, LON824Eds: APNewsNow.
Only Bournemouth (8), West Bromwich Albion (8) and Swansea City (7) have a worse record at home, but no side has conceded as many goals at their own ground as Watford.
Elias Kachunga's opening goal ended Huddersfield's run of 59 consecutive shots away from home in the Premier League without scoring.
Ninth-place Watford has now lost three league games in a row and four of its last five.
The Terriers had gone eight games in League and League Cup since their last goal on the road, in their 3-0 victory at Crystal Palace on opening day.