An early Josh Turnbull try put the hosts in the ascendant at BT Sport Cardiff Arms Park and it was a lead they never surrendered to their rivals.
Gareth Anscombe kept the scoreboard ticking and Rey Lee-Lo crossed on the stroke of half-time as the Blues opened up an 18-8 lead.
They enjoyed some bright spells in the second-half and often attacked at will but could not make the last pass or kick stick.
But with the last play of the match Anscombe parted the Dragons defence for a stunning score he then converted.
The only downside was the failure to secure a try-scoring bonus-point but with Munster and Edinburgh losing earlier in the weekend, the Blues are now just one point off sixth.
The Dragons enjoyed the early possession and territory but the Blues soaked up the pressure and launched their first attack through Tom James.
James broke off first phase ball from a solid scrum and the hosts soon cleared deep into the Dragons 22.
Ellis Jenkins piled the pressure on the Dragons as he charged down Sarel Pretorius’ box kick and from there Cardiff turned the screw.
They were unable to reap rewards initially but from an ensuing scrum they went through the phases and Turnbull powered over.
Anscombe failed to add the extras from wide but he made amends five minutes later when he booted his side into an 8-0 lead.
Hallam Amos was lively for the Dragons and combined with Pretorius but Dan Fish covered to make a try-saving tackle.
Moments later the Wales wing was on the attack again but he squandered a two on one as the Blues defence refused to buy his dummy.
The Dragons did however hit back through the boot of Dorian Jones on 18 minutes but Anscombe cancelled that out with a shot of his own to make it 11-3.
Amos continued to cause the home defence problems with some strong carries but the Blues scrambled well to hold on.
However they could not clear far and the Dragons rumbled over from a driving lineout with scrum-half Pretorius the beneficiary.
Jones pushed his conversion wide but the try cut the lead to three points with six minutes of the half remaining.
Danny Wilson’s men continued to attack and on 38 minutes Rhys Patchell sliced through the Dragons defence and looked inside to find Sam Warburton.
However Pretorius got a hand to the ball to save the day, albeit at the cost of a penalty and a yellow card.
The Blues kicked to the corner and although they could not drive over from the lineout, an Anscombe dink unlocked the Dragons rush defence with Lee-Lo collecting spectacularly to score under the sticks.
Anscombe slotted the simple conversion to hand the Blues a well-deserved 18-8 lead at the interval.
They continued to attack with aplomb in the second-half with Patchell particularly lively but on each occasion the last pass went begging.
That was the case once again when some fine work from Tomos Williams, on for Lloyd Williams, and Anscombe saw Garyn Smith released.
He moved the ball to James, but the electric wing, who is in search of his 50th
try for the region, could not hold onto the ball. Anscombe however kept the scoreboard ticking as the hosts took control of the encounter.
The Blues were stringing together some stunning phases of play with their willingness to move the ball and they continually knocked on the Dragons door but were unable to cross the whitewash.
They weathered a sustained period of Dragons pressure mid-way through the half before finishing strong.
With just over five minutes left Anscombe knocked a penalty into the corner and the pack powered forward.
Again they were held at bay but in the dying moments Williams made inroads on the right wing before Anscombe sliced through the midfield to claim a converted try.
15 Rhys Patchell (A Summerhill 55), 14 Dan Fish, 13 Garyn Smith, 12 Rey Lee-Lo, 11 Tom James, 10 Gareth Anscombe, 9 Lloyd Williams (T Williams 40); 1 Gethin Jenkins (c) (B Thyer 71), 2 Kristian Dacey (M Rees 55), 3 Taufa’ao Filise (D Lewis 60), 4 Jarrad Hoeata, 5 James Down, 6 Sam Warburton, 7 Ellis Jenkins, 8 Josh Turnbull
16 Matthew Rees, 17 Brad Thyer, 18 Dillon Lewis, 19 Josh Navidi, 20 Manoa Vosawai, 21 Tomos Williams, 22 Harri Millard, 23 Aled Summerhill
8 mins: Try- Josh Turnbull 5-0
13 mins: Pen - Gareth Anscombe 8-0
18 mins: Pen - Dorian Jones 8-3
29 mins: Pen - Gareth Anscombe 11-3
33 mins: Try - Sarel Pretorius 11-8
40 mins: Try - Rey Lee-Lo 16-8
40 mins: Con - Gareth Anscombe 18-8
52 mins: Pen – Gareth Anscombe 21-8
80 mins: Try – Gareth Anscombe 26-8
80 mins: Con – Gareth Anscombe 28-8