Since suffering a knee injury against Bristol City last month, Brown struck with his eighth goal of the season from 20 yards in the 31st minute, off the back of an assist from Mooy.
Huddersfield had gone into the game knowing that a win would secure them a place in the play-offs as they responded in style after losing 4-1 at home to Fulham last time out.
Wolves slipped to only their third defeat in 11 matches but again toiled in front of their own fans but failed to score for the third successive home game.
The hosts were forced into a late change when goalkeeper Andy Lonergan was injured in the warm-up and was replaced by Harry Burgoyne.
But it was Burgoyne's opposite number, Danny Ward, who was first into action when he did well to hold on to a near-post header from Dave Edwards in the 10th minute.
Huddersfield's reaction to that let-off was instant and should have led to them taking the lead only for Nahki Wells to blaze over the bar from 14 yards.
Wells was then presented with another chance after a cross from former Wolves winger Rajiv van La Parra, in the 23rd minute, and although this time he managed to get his shot on target, it was comfortably dealt with by Burgoyne.
Brown then showed Wells the way to goal in stunning style after being fed by Mooy.
Attacker Brown let fly from 20 yards and the ball whistled past Burgoyne's outstretched right hand.
Wolves sought a quick response and would have got one but for Ward, who again saved a header from Edwards after a Ben Marshall free-kick.
Ward and the post then combined to deny Wolves an equaliser eight minutes into the second-half when Andreas Weimann had his shot saved and from the follow-up, Edwards saw his effort from an acute angle hit the woodwork.
But their hopes of a comeback hopes should have been extinguished in the 69th minute only for substitute Collin Quaner to drill his shot wide after Wolves had failed to clear a Mooy free-kick.
Quaner then shot straight at Burgoyne from close range 10 minutes later and had a third effort blocked but Wolves were unable to take advantage of his profligacy in front of goal.
