David Wagner's side had dropped to the foot of the table after Fulham's win over Southampton on Sunday, but the congested nature of the league's bottom half means that a second victory in three games lifts them up to 14th.
Mooy's first came after just six minutes – a cool finish from 20 yards to open his account for the season – and the Australia international whipped in a fine free-kick from a similar distance in the 74th minute to seal all three points.
Wolves – who saw a Raul Jimenez effort hooked off the line in the second half – looked a shadow of the side that started the season so well and have now gone five games without a win.
Huddersfield started with a spring in their step and was rewarded with the opening goal. Erik Durm's low cross from the left was met on the edge of the penalty area by Mooy, who slotted into Rui Patricio's bottom-right corner.
Wagner's side comfortably kept Wolves at bay for the remainder of the first half and Steve Mounie could twice have doubled its advantage before the break.
He saw two headed efforts denied, the first repelled by Patricio from Mooy's corner and the other blocked in front of goal by Matt Doherty.
Wolves thought they had pulled level after 56 minutes, but Philip Billing acrobatically hooked clear Jimenez's header before the whole ball had crossed the line.
Billing then shot wide at the other end before Jimenez wasted a golden opportunity to equalise, poking well wide with only Jonas Lossl to beat.
That miss was brought into sharp focus 16 minutes from time when Mooy curled a 20-yard free-kick inside Patricio's left-hand post to wrap up a deserved victory for the revitalised Terriers.