Tom Elliott scored twice and Andy Robinson scored the other as the Whites moved two points clear of their hosts with two matches of the season remaining, both against Rotherham.
United's run of victories has left them in control of the race of the league title, and last night's success inflicted Town's first defeat of the campaign.
Thompson had the luxury of a strong line-up, with two players, Robinson and Andrew Hughes, both appearing 24 hours after United's 2-2 draw at Leyton Orient on Tuesday night.
As well as those two, Frazer Richardson, Lubo Michalik, David Prutton and Bradley Johnson made Town do the chasing as they quickly established control.
Hughes made Elliott's seventh-minute opener, supplying a cross which the striker neatly despatched and Robinson added a second goal when he drove home a scorcher from long range on 36 minutes.
In the second half Town nearly got themselves back in the game when an unmarked Lionel Ainsworth missed an easy looking eight-yard header from Dominik Werling's 47th-minute cross.
But David Lucas was tested only one more time when he turned an Aiden Chippendale effort into the side netting 13 minutes from the end.
Then Huddersfield were caught out again on 81 minutes when Robinson gave Elliott a simple chance to seal victory after a lovely through ball.
Leeds suffered a slight injury blow when left-back Aidan White limped out at half-time, while Tom Lees also sustained a knock early in the second half, but Thompson was able to give 90-minute run-outs to seven senior players.
Club captain Richardson took another step towards full match fitness with a confident display at right-back.
Leeds conclude their reserve campaign with back-to-back games against Rotherham United, away on April 14 and then at home on April 28.
Town: Eastwood, Hunt (Watson 75mins), Werling, Holdsworth, Ridehalgh, Lucketti, Ainsworth (Atkinson 70), Berrett, Heagney, Craney, Chippendale (Nightingale 83).
Leeds: Lucas, Richardson, Lees (Milne 53), Michalik (Falkingham h/t), White (Darville h/t), Prutton, Johnson, Hughes, Robinson, Grella, Elliott.