The Australian, who this summer turned a loan from Manchester City into a permanent signing that could rise to £10 million, smashed in a 50th-minute winner following a one-two with Elias Kachunga as the Terriers defeated one of the sides they came up with last term.
It meant David Wagner's men followed up last weekend's 3-0 victory at Crystal Palace with another three points to become just the third newly-promoted side to win their first two games in the Premier League era, emulating Bolton in 2001 and Hull last season.
Mooy's long-range shot provided Rob Elliot with his first test and the Newcastle keeper was grateful Tom Ince's vicious try, which came courtesy of a mislaid Christian Atsu pass, was straight at him.
Jan Kruger/Getty Images Ayoze Perez laid the ball off to him on the edge of the area and the winger's effort was heading straight for the bottom corner only for Jonas Lossl to produce a fine one-handed save to tip it around the post.
There were half-hearted penalty appeals at the other end when Atsu's header hit the back of Chris Lowe's arm, not that he knew anything about it, and the Terriers full-back was then bailed out by two fine Christopher Schindler tackles, the second of which had to be timed right on Dwight Gayle.
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