Llanelli's star striker Griffiths sparked their challenge with a strong run down the right followed by a rasping shot that forced a low save from Scott James.
Griffin fired wide across the face of the goal, before a skidding Hughes shot made Reds goalkeeper Ryan Harrison scrabble the ball away for a corner, ensuring a goal-less first half.
Straight from the restart, Griffiths scythed through a sleeping home defence, his toe poke bouncing clear off the legs of the unsuspecting James.
Griffiths' miss was soon outdone by Griffin at the other end, a poorly defended free kick falling straight to his feet in the six-yard box only for the usually prolific striker to spoon the ball over the bar.
A swift excursion out of his area by Harrison was enough to scupper a Hughes chance, and the Reds keeper was again on hand to comfortably gather a header from the striker.
The game seemed to be heading for extra time, but with nine minutes left a swinging Newport corner found the outstanding Jarman.
He powered a header into the ground, a committed Hughes powering onto it past a static Reds defence to finish from close range.
Hughes nearly extended the lead with a header from Jason Bowen's cross, and a last-gasp equalising chance from Antonio Corbisiero flew just wide of the County post.
This was Newport's third Premier Cup final - having lost to The New Saints last year and Wrexham in 2003 - and the Cup provides manager Peter Beadle's first silverware in two-and-a-half years at the club.
Llanelli still have the chance of securing a treble as they top the Welsh Premier, are in the final of the Loosemores League Cup, and the semi-finals of the Welsh Cup.
The future of the FAW Premier Cup competition is uncertain, though, as BBC Wales will not continue its sponsorship next season.
Newport:
Scott James, Steve Jenkins (capt), Lee Jarman, Paul Cochlin, Damon Searle, Jason Bowen, Andy Gurney, Nathan Davies, Richard Evans (Lee Fowler 80), Craig Hughes, Charlie Griffin (Jermaine Clarke 75).
Llanelli:
Ryan Harrison, Stuart Jones, Lee Phillips (capt), Andrew Mumford, Gary Lloyd, Craig Jones, Chris Holloway, Antonio Corbisiero, Andy Legg, Mark Pritchard, Rhys Griffiths.
Referee:
Lee Evans
