After Elias Kachunga gave the visitors the lead - shortly before being stretched off with a leg injury - Mooy then added a double either side of a Laurent Depoitre goal, as Huddersfield cruised to victory in Hertfordshire.
Terriers razor sharp
The Terriers looked sharp from the off and capitalised on an early spell of dominance to take the lead. Heurelho Gomes denied Colin Quaner from close range, allowing Kachunga to grab his first Premier League goal with a simple tap-in.
The Congolese attacker appeared offside, much to the frustration of the Hornet's fans and players. However, Kachunga, unfortunately, had to be stretchered off soon after following an injury to his left knee.
The Terriers' commanding spell maintained through the ensuing minutes. It wasn't long before the second flew in. Mooy continued a remarkable first season in the Premier League to grab his third goal of the season.
Meeting a beautiful cross across the box from Quaner, the Australian's chest connected to double the lead for the visitors.
Things went from bad to worse soon after for Marco Silva's men. Captain Troy Deeney saw red after a reckless challenge on Quaner, his first in over four years.
Things continued much of the same early in the second half, and just four minutes after the restart, Depoitre fired Wagner's side further ahead.
Gomes could do precious little to stop the driven strike from a tight angle, and things looked comfortable for Huddersfield.
That was until Jonathan Hogg received his marching orders. The former Watford man captained Town in the absence of Tommy Smith, missing out through illness.
Richarlison was brought down by the Town captain, who had already been booked. The Watford players hounded Michael Oliver, who eventually brought out the red card to even the numbers on the field.
As the clock hit 61 minutes, there was still plenty of time for a revival from the home side.
What followed was a resurgence from the home side. Florent Hadergjonaj was called into immediate action, firstly to block out a swinging Holebas cross, before combining with Jonas Lössl to keep a clean sheet intact.
And yet, Abdoulaye Doucouré found the opening strike for Watford, a thunderous half-volleyed strike from twenty yards for his sixth of the campaign.
The pressure was piled on the visitors. Successive chances for Andre Gray and Richarlison tested the nerves of the Terriers' back line.
The game was wrapped up in the 88th minute through a brilliant penalty from Aaron Mooy.
Doucouré brought down Depoitre in the area, and Mooy seized the opportunity to finish off the game.
The bottom corner bulged as Mooy struck past Gomes, snatching all three points for a famous victory on the road.