The Terriers winger crashed home the all-important 54th minute winner to deny Swansea in their bid to return to the top of League One.
Danny Cadamarteri's surging run and cross found its way to Kamara, who prodded home from close range at the second attempt.
Swansea rung the changes following their exploits in the cup competitions, with manager Roberto Martinez being able to call upon the fit-again Ferrie Bodde in midfield.
Huddersfield had to do without the services of captain Jon Worthington, while prolific striker Luke Beckett had to make do with a place among the substitutes.
In a scrappy opening, Swansea finally found their feet and Darryl Duffy was inches away from converting Angel Rangel's cross at the near post with 12 minutes on the clock.
And Swans striker Duffy came even closer to breaking the deadlock moments later, latching onto Jason Scotland's through ball before stinging the palms of visiting goalkeeper Matt Glennon.
Huddersfield finally mustered a chance of their own in the 30th minute and only a brilliant save from Dorus de Vries kept out Andy Booth's downward header following Joe Skarz's in-swinging corner.
Attacks from both sides broke down all too frequently in the heavy rain, although Thomas Butler's long-range volley sailed just over Glennon's crossbar just before the break.
But in a rare foray forward, the Terriers took the lead in the 54th minute through Kamara's low shot.
Cadamarteri's surging run and cross saw Danny Schofield's shot blocked by de Vries but straight into the winger's path for the game's opening goal.
Swansea looked for an immediate response, but Scotland could only slice his 25-yard shot wide before Duffy was once again off-target.
Duffy and Scotland were again thwarted by Glennon before Garry Monk's header was chalked off for pushing at the death.