Town were rewarded for their greater control and threat when the outstanding Mooy smashed a 25-yard shot into the top corner after the break.
Leeds, who slip to third from bottom with just one win from their first six league fixtures, rarely threatened.
Town held on to go four points clear thanks to a fifth win from six.
On-loan Manchester City midfielder Mooy was not certain to play after a hectic international break which saw him appear in both of Australia's World Cup qualifiers.
But he dictated the play as the Terriers had the better of a dull first half in which neither side could muster a shot on target.
Mooy, who was booked late in the first period for a nasty-looking lunge that infuriated Leeds manager Garry Monk and his coaching staff, came closest with a decent low strike.
But his second attempt on goal 10 minutes after the restart proved much more successful and was reward for the visitors' urgency and superior quality.
Chris Wood sent a header wide for Leeds before the break and could have snatched a barely deserved point late on, but failed to properly connect with another headed opportunity.
Leeds head coach Gary Monk:
"I'm disappointed with the result, of course. We went out there with the intention of trying to grab the initiative but partly due to the way (Huddersfield) set up it became a bit of a nothing game.
"We have to get a real reaction now on Tuesday. We need to take the three points, it's as simple as that.
"It's very important that we get this Elland Road monkey off our backs and get the three points."
Huddersfield head coach David Wagner:
"There is every reason to be surprised. I don't know which team in this division can say they will start with 16 points after six games.
"We have deserved every one of the 16 points and we said at the start of the season we would play every single game and give ourselves no limits and at the moment we have great togetherness and a very good working attitude, especially in the defence.
"I think it isn't comfortable for the opponents against us at the moment."
Match ends, Leeds United 0, Huddersfield Town 1.
Second Half ends, Leeds United 0, Huddersfield Town 1.
Substitution, Huddersfield Town. Michael Hefele replaces Harry Bunn.
Foul by Rajiv van La Parra (Huddersfield Town).
Kyle Bartley (Leeds United) wins a free kick on the right wing.
Chris Löwe (Huddersfield Town) wins a free kick in the defensive half.
Foul by Kemar Roofe (Leeds United).
Mark Hudson (Huddersfield Town) wins a free kick in the defensive half.
Foul by Souleymane Doukara (Leeds United).
Foul by Harry Bunn (Huddersfield Town).
Kalvin Phillips (Leeds United) wins a free kick in the defensive half.
Corner,  Huddersfield Town. Conceded by Robert Green.
Attempt saved. Rajiv van La Parra (Huddersfield Town) right footed shot from more than 35 yards is saved in the top centre of the goal.
Attempt saved. Chris Wood (Leeds United) header from the centre of the box is saved in the bottom right corner. Assisted by Alex Mowatt.
Chris Löwe (Huddersfield Town) wins a free kick on the left wing.
Foul by Kemar Roofe (Leeds United).
Chris Löwe (Huddersfield Town) is shown the yellow card.
Attempt missed. Kasey Palmer (Huddersfield Town) right footed shot from outside the box is just a bit too high.
Mark Hudson (Huddersfield Town) wins a free kick in the defensive half.
Foul by Souleymane Doukara (Leeds United).
Delay over. They are ready to continue.
Delay in match Liam Bridcutt (Leeds United) because of an injury.
Tommy Smith (Huddersfield Town) wins a free kick on the right wing.
Foul by Alex Mowatt (Leeds United).
Substitution, Huddersfield Town. Kasey Palmer replaces Jack Payne.
Chris Löwe (Huddersfield Town) wins a free kick in the defensive half.
Foul by Kemar Roofe (Leeds United).
Substitution, Huddersfield Town. Nahki Wells replaces Elias Kachunga.
Delay over. They are ready to continue.
Delay in match Christopher Schindler (Huddersfield Town) because of an injury.
Substitution, Leeds United. Kemar Roofe replaces Hadi Sacko.
Pontus Jansson (Leeds United) is shown the yellow card.
Rajiv van La Parra (Huddersfield Town) is shown the yellow card for a bad foul.
Foul by Rajiv van La Parra (Huddersfield Town).
Alex Mowatt (Leeds United) wins a free kick in the defensive half.
Harry Bunn (Huddersfield Town) is shown the yellow card for a bad foul.
Foul by Harry Bunn (Huddersfield Town).
Charlie Taylor (Leeds United) wins a free kick on the left wing.
Attempt saved. Alex Mowatt (Leeds United) left footed shot from the left side of the six yard box is saved in the bottom right corner.
Substitution, Leeds United. Souleymane Doukara replaces Marcus Antonsson.
Aaron Mooy's spectacular long-range strike earned unbeaten Championship leaders Huddersfield Town victory over struggling west Yorkshire rivals Leeds.