The home side's 29-year-old fly-half, Byron Hayward, kicked four penalties and a conversion to strengthen further his chances of making a debut appearance in the Wales side against Scotland at Wembley on Saturday.
Vale also scored two tries - from the wing Alun Harries and the centre Jonathan Hawker - while Cardiff's points were all supplied by the boot of their fly-half Lee Jarvis who landed three penalties.
In the quarter-finals, Ebbw Vale will have the opportunity to create another upset when they play host to the current Premier Division leaders Swansea, who yesterday coasted to a 66-12 home victory over the First Division side Aberavon, thanks largely to a haul of four tries from their centre Mark Taylor.
Giantkillers Garndiffaith, who have already disposed of Bridgend this season, extended their amazing cup run into the last eight, although they had to endure eight minutes of injury time, with a 19-14 home win over Second Division Llanharan.
Seven Sisters joined their fellow Fourth Division side in the last eight with a 15-11 victory away to the Second Division leaders Tredegar, and their reward was a quarter-final draw away to Garndiffaith.
Newport cruised into the last eight with a 69-15 romp away to Uwic - a match which yielded no fewer than 13 tries. Ten of those touchdowns went Newport's way with the centre David Smith helping himself to a hat- trick.
The writing was on the wall as early as the third minute when Jan Machacek, Newport's Czech back-row forward, drove through the students' defence for the game's first try. Uwic claimed three tries of their own but the power of the Premier Division side's pack proved decisive.
There was a predictable home win for another Premier Division side, Neath, who prevailed 41-0 against Builth Wells, but Pontypridd had to rely on an injury-time try from their New Zealand flanker Dale McIntosh to seal a 33-24 success at Abertillery and an away draw at Newport. Neil Jenkins, who told the Wales coach Kevin Bowring that he no longer wished to play at full-back following his humiliation by England, kicked 13 points, but was outshone by his rival fly-half, Phil Whithers, who ran in two tries.
Neath must await the outcome of today's tie between Llanelli and the First Division leaders Caerphilly to know where they will be playing next.
SWALEC CUP quarter-final draw: Seven Sisters v Garndiffaith; Llanelli or Caerphilly v Neath; Ebbw Vale v Swansea; Newport v Pontypridd. Matches to be played on 11 and 12 April.Reuse content