Cardiff made good use of the strong wind in the first half as Gareth Davies landed four penalties to one from Jordan Williams for the visitors. The first try of the game came just before the break when the visitors were reduced to 14 men with Shaun Hopkins in the sin bin and the home pack produced a strong scrum to claim a penalty try.
Davies added the conversion to make it 19-3, but then saw his game come to a premature end with an injury as the half-time whistle went. That left the goal kicking duties for the home side resting on the shoulders of Scott Sneddon
Llanelli drew first blood in the second half with Williams' second penalty, but the Blue and Blacks moved further ahead when
Wales Under 20 back row man Dan Crimmins pounced on a loose ball and started a move which ended with Robinson crossing for a try which Sneddon converted to make it 26-6.
But the visitors staged a magnificent fightback and two tries in the space of six minutes from Owen Williams and Bowdy Davies, both converted by Williams, cut the gap to a mere six points.
Now it was anyone's game, but Sneddon kept his nerve to land a touchline penalty and then hoist his match tally to 11 points with two more goals before the end. Williams ended with 19 points, from two conversions and five penalties, but it wasn't enough to win the day.
A brilliant second-half comeback saw Neath claim a 20-14 victory at Bridgend Athletic after they had trailed by 14 points at the break. Two penalty tries helped the fight-back after the home side had raced into a commanding lead with tries from Johnny Phillips and Stuart Edbrooke.
Three Gwent clubs reached the quarter-finals with two of the teams coming from Division 1 East. Ebbw Vale had already dumped Newport out of the tournament and the Steelmen added the scalp of Carmarthen Quins to their collection with a 16-3 triumph at Eugene Cross Park.
Outside half Dorian Jones was the home hero as he kicked 11 points, including a 60 metre penalty, and the Quins were forced to head home with their tails between their legs after also conceding a second half penalty try.
Former Wales Under 20 outside half Dean Gunter kicked 26 points as Cross Keys beat Rumney 36-18. Full-back Steffan Jones and wing Marcus Johnstone both crossed for tries to help steer the home side in the last eight.
Newbridge came out on top in their all Division 1 East clash with Bargoed. Flanker Dean Gibbs scored the only try of the game as Bargoed were defeated 13-3. Neil Burnett added a conversion and a penalty for the home side and Josh Prosser's penalty was Bargoed's only score.
Beddau's clash with Swansea, UWIC's visit to Ammanford and the all Premiership clash between Pontypridd's and Tonmawr were all postponed.
SWALEC CUP SCORES
Bridgend Ath 14 20 Neath
Cardiff 35 29 Llanelli
Cross Keys 36 18 Rumney
Ebbw Vale 16 6 Carmarthen Quins
Newbridge 13 3 Bargoed
Ammanford P P UWIC
Beddau P P Swansea
Pontypridd P P Tonmawr