Sixth-placed Huddersfield was expected to make light work of a struggling Wigan outfit at home, but it was the visitor which struck first, against the run of play, through on-loan West Ham defender Reece Burke.
The right back pounced on some loose possession, before backing up to rifle home Yannick Windschut's deflected cross.
Australia midfielder Mooy brought Huddersfield level with a neat finish to complete a 12-pass move, more indicative of Huddersfield's dominance.
But it was the visitor, in its first match under ex-Manchester United reserves coach Warren Joyce, which had the last laugh.
Wildschut pounced on another Terriers error, before being played in behind, skilfully rounding Danny Ward and sending his team into a match-winning lead.
More to come..