The Terriers made a strong start at Molineux Stadium and went ahead in the sixth minute when Mooy applied the finishing touch to Erik Durm's cut-back.
Rui Patricio was twice called into action as Huddersfield Town pushed for a second, first saving from Terence Kongolo and then Steve Mounie.
Wolves thought they had equalised in the 57th minute, but Philip Billing hooked a header from Raul Jimenez off the line.
Mooy then doubled Huddersfield Town's lead with a brilliant 74th-minute free-kick to lift them from bottom to 14th place in the table on 10 points.
A fourth defeat in five matches leaves Wolves 11th with 16 points
Wolves: 30 Nov v Cardiff (A)
Town: 1 Dec v Brighton (H)