The win also meant Andy Ritchie's side kept a fourth clean sheet in a row for the first time in eight years.
Only 43 seconds had elapsed when Jevons capitalised on a poor clearance from Jerel Ifil to delicately place his shot past helpless goalkeeper Petr Brezovan.
Huddersfield shaded a first half short on quality and goalmouth action and man of the match Andy Holdsworth was at the heart of the home side's best moves.
His forceful prompting from midfield led to Jevons shooting over the top.
However, Swindon came out all guns blazing in the second period and nearly levelled through Sofiane Zaaboub.
Christian Roberts evaded the attentions of left-back Robbie Williams on the right wing to float a sumptuous ball to the back post for the unmarked Zaaboub, but his left-foot effort drifted inches wide.
A lovely defence-splitting pass from Huddersfield winger Danny Schofield then allowed Luke Beckett a rare sight at goal.
Town's top-scorer looked odds-on favourite to double the host's advantage, but he fluffed his one-on-one chance against Brezovan by firing wide of the right-hand post.
Michael Collins went close to extending Huddersfield's winning margin with 12 minutes left.
The 21-year-old midfielder's dipping cross had the home fans briefly on their feet, but the ball dropped agonisingly onto the top of the net.
Swindon could have snatched a last-gasp equaliser courtesy of captain Hasney Aljofree.
The towering defender powered past Huddersfield's tiring defence only to thump his shot over the bar with the goal at his mercy.