Jason Scotland kept the Swans on Championship course with a first-half winner that sent Roberto Martinez's side 14 points clear at the top.
Scotland scored his 21st goal of the season in the 45th minute as the Swans battled back from an ever-increasing injury list to end their Huddersfield hoodoo at the Glapharm Stadium.
To make matters worse for the home side, they had Welsh international Robert Page sent-off eight minutes from time for a second yellow card.
Huddersfield: Glennon, Sinclair, Page, Clarke, Williams, Kamara (Schofield 81), Holdsworth, Collins (Mirfin 90), Brandon, Jevons (Booth 78), Beckett. Subs Not Used: Eastwood, Skarz.
SwanseaCity: De Vries, Rangel, Tate, O'Leary, Austin, Butler, Bodde, Britton, Pratley, Robinson (Brandy 46), Scotland (Duffy 90). Subs Not Used: MacDonald, Way, Burgin.
Att: 10,471
Ref: M Oliver (Northumberland).
The Swans were delivered a late blow when skipper Garry Monk pulled out with a back injury sustained in training on Thursday.
It left Swansea short at the back with Dennis Lawrence (knee) and Marcos Painter (hamstring) already ruled out.
It meant midfielder Kristian O'Leary was drafted in at centre-half to partner Alan Tate, while Angel Rangel and Kevin Austin took up the full-back berths.
It also saw a late call-up for 18-year-old left-back James Burgin from the youth team as cover on the bench. Burgin, from Derby, had been on loan at Port Talbot.
Although Paul Anderson still hadn't recovered from his hamstring strain, midfielder Ferrie Bodde and Leon Britton returned from injury as Roberto reverted to his preferred 4-5-1 formation.
The Terriers, who had beaten the Swans on their last four trips to Yorkshire, started with a 4-4-2 formation.
After a scrappy start to a game played in windy conditions, the Swans started to keep possession well before Bodde forced Matt Glennon into the first save of the game with a shot that the 'keeper pushed around the post.
Playing with the strong wind at their backs, Swansea remained on top as Scotland forced Glennon into his second save with 12 minutes gone.
Huddersfield responded through Michael Collins who fired just over the bar before Brandon forced Dorus de Vries into his first save.
The home side started to come more into the game with 20 minutes gone, although it was Andy Robinson who came close next up as he forced Glennon to push another effort around the post.
Phil Jevons back-heeled an effort just wide minutes later before Robinson Glennon with a near-post effort after a good pass from Scotland.
But as the two sides prepared to go in at the interval on even terms Swansea, who had had by far the better of the first-half, struck before the referee could blow his whistle.
With the game two minutes into injury time, Bodde's corner was not cleared and Alan Tate flicked the ball on where Jason Scotland fired home from close range.
It was the first time Huddersfield had conceded a goal at home in four games.
Half-Time: Terriers 0 Swans 1
Swansea made a change at the start of the second-half as Febian Brandy came on for the injured Robinson.
Brandy was straight in the action as he had an effort blocked by Williams, before Jevons missed a great chance in the 48th minutes when he volleyed over a Luke Beckett header.
Swansea had to defend well as the strong wind made it difficult, as Robbie Williams fired a long-range free-kick over the bar before Jevons forced De Vries into a near-post save.
De Vries pulled off another save from Andy Holdsworth before making an even better stop when Chris Brandon latched on to an Angel Rangel back-pass.
The Terriers were now throwing everything at the Swansea defence as Williams volleyed wide and Beckett headed just passed the post.
Robert Page was booked after 76 minutes for a foul on Brandy. Six minutes later and his second yellow turned into a red after pulling back Scotland.
It unsettled the home side and Brandy came close before Glennon made a point-blank save from Scotland in the last minute. Tom Butler followed up to fire home the rebound, but the winger was ruled offside.
Scotland was hurt in the process and replaced by Darryl Duffy as Swansea stretched their unbeaten run in the League to 18 games.
