The victory is Huddersfield's first since October 23, after a five-game run that saw Town lose three times and draw twice.
Mooy was at the heart of the action with 72 passes, and three tackles, including one that led to the opening goal.
The former Melbourne City winger stopped Bristol City's Marlon Pack from launching an attack with a well timed tackle before laying the ball off to Elias Kachunga who scored the opening goal.
There was vast praise for the Socceroos midfielder on social media after the match.
The victory sees Huddersfield move up to fourth on 33 points, ten behind leaders Newcastle United.
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