Phil Jevons struck the only goal of the game in the first minute as Huddersfield ended Swindon's nine-match unbeaten run in League One.
Jevons had plenty of time to slot home inside the six-yard box after a defensive howler from Jerel Ifil.
Swindon almost equalised after 56 minutes but Sofiene Zaaboub dragged his shot wide after a superb cross from Christian Roberts.
Luke Beckett should have added a second for the hosts but fired wide.
Huddersfield: Glennon, Sinclair, Clarke, Page, Williams, Collins (Mirfin 90), Worthington (Kamara 75), Holdsworth, Schofield (Brandon 70), Beckett, Jevons.
Subs Not Used: Booth, Smithies.
Goals: Jevons 1.
Swindon: Brezovan, Comminges, Ifil, Aljofree, Vincent, Roberts (McNamee 86), Peacock, Zaaboub (Sturrock 75), McGovern, Cox, Ashikodi (Pook 45).
Subs Not Used: Phil Smith, Kanyuka.
Booked: Vincent, Cox.
Ref: Fred Graham (Essex).