It was an important victory for the fifth-placed Terriers who are now only eight points off top spot.
However, it could've been a very different story for Mooy after a mistake by the Socceroos star gifted Brighton an equaliser after 20 minutes.
Going up for the ball in midfield, Mooy mistimed his header and knocked it past the Huddersfield defence and into the path of Brighton striker Tomer Hemed. The marksman rounded keeper Danny Ward to level the score at 1-1.
The mistake failed to hold Mooy back with the 26 year-old rebounding in impressive style.
Only 16 minutes later Mooy was involved in a slick passing move which opened up the Brighton defence and gifted Nahki Wells a goal to give the David Wagner coached side the lead.
It didn't end there for the former Western Sydney Wanderers and Melbourne City player as he delivered another pinpoint pass to send Wells through, followed by a classy Elias Kachunga finish, to give Huddersfield a 3-1 lead at the break.
A raking low drive from 25 yards out nearly put Mooy on the scoresheet in the second half but he was denied by the woodwork.
Brighton's hopes of a comeback were ultimately ended when Lewis Dunk received a second yellow card with 20 minutes left on the clock for a lunge on Isaiah Brown.
Mooy's name was sung by the Huddersfield faithful as the Terriers clung onto victory with his first half misdemeanor well and truly forgotten by the fans.