Andre Ayew, Jay Fulton and Jordon Garrick were on target as Swansea won for the first time in six league games.
Steve Cooper’s side led after top scorer Ayew pounced on a rebound to claim his 13th goal of the season.
Steve Mounie’s close-range strike 12 minutes from time levelled, but Fulton quickly restored Swansea’s lead before Garrick sealed the win on 90 minutes.
With their winless run now standing at three matches, the Terriers are left looking over their shoulders towards the bottom three with a dozen games remaining as they are 21st, while Swansea rise to ninth.
In need of a performance after a poor sequence of results, Swansea looked hungry to turn their form around from the outset.
Barely a minute had passed when Aldo Kalulu beat his man and crossed for Rhian Brewster, whose header was pushed over by Jonas Lossl.
Huddersfield offered almost nothing in the first period, though one swift counter ended with Juninho Bacuna volleying over the top.
Swansea deservedly went ahead on 28 minutes when on-loan Basel winger Kalulu’s shot was parried by Lossl, with Ayew on hand to steer home from close range.
The one first-half frustration for Swansea was that they were not further ahead, with Kyle Naughton driving into the side netting before Brewster went through one-on-one only to see his dinked effort saved by Lossl.
The lively Kalulu sliced a half-volley wide early in the second period, but Danny Cowley made three attacking changes and Huddersfield finally began to ask questions.
Karlan Grant cut in from the left and drove a shot straight at Freddie Woodman, then Richard Stearman headed down the Swansea goalkeeper’s throat.
With the pressure building, the leveller came when Chris Willock’s low shot was turned into the net by fellow substitute Mounie.
But Swansea responded almost immediately, with Fulton nodding home just his second goal of the season from Matt Grimes’ corner.
Conor Gallagher then fed substitute Garrick, who coolly rounded Lossl before steering in his second goal in two games.