The Australia midfielder found the net in each half as the Terriers were deserved winners at Molineux, where the hosts looked off the pace on their return from the international break.
Mooys double was the first time Huddersfield had scored twice in a league game this season and its second win of the campaign lifted David Wagners team up to 14th in the table. Wolverhampton is now without a win in five league games, losing four.
The game started at a frantic pace, with Wolves doing much of the attacking. But it was Huddersfield which took the lead after six minutes.
Matt Doherty failed to track his man, allowing Erik Durm to get in behind the Wolves defense on the left. His low cross went perfectly into the path of Mooy, whose measured side-foot finish flew into the bottom corner of the net, giving goalkeeper Rui Patricio no chance.
For all Woverhamptons dominance in possession, it created nothing in the first half and Huddersfield had chances to extend its lead before the break, with Steve Mounie having three chances in quick succession to get his first goal of the season.
Wolves manager Nuno Espirito Santo made two changes at halftime and only a superb goal-line clearance from Philip Billing denied the hosts an equalizing goal as Raul Jimenezs far-post header from Adama Traores cross was somehow kept out.
Mooy doubled his tally in the 74th minute with a superb curling free kick, bending the ball around the outside of the defensive wall and beating Patricio down by the post.