Joel Piroe’s first-half strike was enough to earn the hosts a 1-0 triumph over the Terriers.
The 22-year-old struck in the 17th minute to give the Welsh side their first home victory of the season.
It was a fourth clean sheet in five games at home for Russell Martin’s men, who crucially found a breakthrough after failing to score in their previous two home matches.
Despite the defeat, Huddersfield remain in seventh place inthe standings, just three points off the play-off places.
Swansea were out to break a run of three consecutive Championship draws after they snatched a point any Luton with a dramatic three-goal comeback in their last league outing.
Despite the defeat, Town boss Corberan was reassured by his team’s overall display.
“I feel we competed better in the second half than we did in the first,” said Terriers manager Carlos Corberan.
“They had more clear chances, but they came from our mistakes. We didn’t find a solution to the way they pressed and we lost organisation in defence for the goal they scored. Until that moment we were doing really well.
“We needed to manage our attack better the second half, we competed better and won more second balls.
“We played more in the offensive half and pressed well too. The mentality in the first half was not good enough.
“In some spaces of the pitch they were better individually than us which didn’t allow us to counter attack. It’s important to compete for 90 minutes.
“We have the intention to dominate the game with the ball but we need to find the balance of playing long and playing short.”
Swans’ boss Martin was forced into a defensive change after both Rhys Williams and Ryan Bennett picked up knocks.
Ryan Manning moved from wing-back into the back three to join Ben Cabango and Kyle Naughton.
Olivier Ntcham returned to an attacking midfield role in place of Liam Walsh and Piroe replaced the injured Michael Obafemi up front.
Swansea had dominated their last home game against Hull but were left frustrated by the Tigers’ stubborn defence, but this time they found the early breakthrough after 17 minutes.
The impressive Jamie Paterson received the ball from Piroe, swivelled and played a delicate pass over the top to find the run of the Dutch striker, who got ahead of Tom Lees and produced a composed finish for his sixth goal of the season.
Chief creator Paterson should have doubled the lead moments later after a defensive mix-up presented him with a clear sight at goal and only Lee Nicholls to beat, but he dragged his effort wide.
Piroe had only scored five goals in his previous 30 senior games before his move to South Wales, but he looked determined to add to his tally. First, he took down a long free-kick, cut in and shot at Nicholls, before forcing the Huddersfield goalkeeper into an acrobatic save down low to his left.
The visitors held out until half-time to go in 1-0 down, but the pressure continued to build after the restart when Flynn Downes shot across goal to force Nicholls into another save.
The visitors had a chance to level when Harry Toffolo headed over from Sorba Thomas’ corner as they began to exert some pressure of their own.
But the Swans resisted to secure their second Championship victory this season.
Swansea City: Hamer, Cabango, Naughton, Manning, Laird, Downes, Grimes, Bidwell, Ntcham (Fulton 76), Paterson (Smith 70), Piroe (Cullen 69). Unused substitutes: Benda, Cooper, Latibeaudiere, Walsh.
Huddersfield Town: Nicholls, Pearson, Lees, Colwill, Turton (Koroma 61), Hogg (Odubeko 83), O’Brien, Toffolo, Sinani, Thomas, Campbell (Holmes 64). Unused substitutes: Vallejo, High, Sarr, Bellagambi.
Referee: G Ward (Surrey).