Tries from Scott Andrews and Phil Williams kept the Blues in touch, but a disallowed try in the final moments cost the visitors victory with Dragons coach Wayne Jones saying; "I'm pleased with the way we battled and to kick off the season on a winning note is a real boost.
"Our set piece was good and though we lost our shape towards the end, I'm sure this will give us the confidence to kick on from here."
Meanwhile the Ospreys failed to use home advantage when they met the Scarlets - a Dean Ronan try and Matthew Jervis conversion was all they could muster against a slick looking Scarlets outfit led by Llanelli's Ricky Guest.
To crown a wonderful night for the Scarlets, who ran out 24-7 winners, they bagged a bonus point too thanks to tries from Neil Davies, James Davies, Joe Davey and Ellis Lloyd.
Daniel Etteridge kicked two conversions for good measure and Scarlets team manager Steffan Thomas said; "When we saw the make up of their side, we realised we were in for a tough night. However, to score four tries and to win with a bonus point is a terrific start for us."
A Jack Roberts try and five points from the boot of Dale Ford made sure of a point for the Scarlets under 18s as they drew 10-10 with the Ospreys.
Tom Priday kicked a penalty for the Ospreys and converted a try from openside flanker Mike Sully. The result means the championship is still wide open with three of the five regions all in with a chance of reaching the final.