Danny Wilson’s men went into the encounter on the back of two consecutive Championship defeats but led 27-16 at the interval.
Steve Shingler scored after just one minute and both Kristian Dacey and Josh Navidi crashed over the whitewash in a dominant second quarter.
But a stalemate ensued following the break and the Blues could never get going in a scrappy second-half.
It took the Blues little more than a minute to open the scoring at a capacity BT Sport Cardiff Arms Park.
Fly-half Shingler took the ball to the line and dummied past the Dragons defence to stretch over in the corner. He then converted from the touchline.
Angus O’Brien hit-back with the boot after the Dragons earned a scrum penalty on 12 minutes and he slotted a second after Rey Lee-Lo was harshly sin-binned for a high tackle.
The Dragons were soon also down to 14-men after Rynard Landman was shown yellow for a shoulder charge on Alex Cuthbert at the breakdown.
Shingler duly converted to make it 13-6 but the visitors quickly drew level with a neat converted try.
With the Blues’ backline stretched, O’Brien dummied and then dinked a perfectly-weighted grubber through for Hewitt to collect.
The try kicked Cardiff Blues into life and they enjoyed a sustained period of pressure in the Dragons twenty-two.
Finally, cracks appeared in the Dragons’ defence and after Nick Williams went close from a five-metre scrum, Dacey twisted over.
Shingler converted to bring the scores to 20-13 and while O’Brien kept the scoreboard ticking, Wilson’s men grabbed a third before the break.
They dominated the closing stages and Shingler sliced through the visitors’ defence before sending Navidi under the sticks for a 27-16 half-time lead.
The Blues started the second-half well, with the pack flexing their muscle at scrum-time but a scintillating counter-attack from Ashton Hewitt set alarm bells ringing.
He was eventually put to a halt but the Dragons held onto possession and turned the screw. They kicked two penalties to the corner but were unable to break down the Blues’ defence.
After weathering the storm, Cardiff Blues reaffirmed their strong-hold on the encounter. But despite promising periods of possession, the last pass failed to stick on several occasions.
Matthew Morgan was narrowly off-target with a penalty attempt on 66 minutes, while Shingler was receiving treatment.
The Blues pressed throughout but the game was littered with errors, and the game ended 27-16 for a crucial home victory ahead of a trip to Scarlets on New Year’s Day.