However, it wasn't easy and the Cell C Sharks had to fight back with two converted tries in the last 18 minutes to come away with the win in Wales.
The home side, coming from an away win against a strong Munster side last weekend, showed their intent by winning the first lineout on a Cell C Sharks throw-in and had the best of the first 40 minutes.
The Dragons held their own up front and were threatening in the one or two backline moves, but were unable to breach the Cell C Sharks defence in a somewhat scrappy match.
The home side led 12-6 at the break with the Cell C Sharks conceding a number of penalties at the scrum and the breakdown.
They seemed to have new energy after the break, but unforced errors kept the Durban side from adding to their score.
On the other hand, the Dragons, after weathering the Cell C Sharks’ storm, drove over from a lineout with flanker Elliott Dee being credited with the try, converted by 20-year-old Will Reed in his debut match.
At 19-6 after 48 minutes play the Cell C Sharks were in trouble, but an intercept try from nearly 50 metres out by Springbok scrumhalf Grant Williams in the 53rd minute, converted by Boeta Chamberlain (flyhalf), brought them back into the match at 19-13.
There was new life and rhythm in the Cell C Sharks backline, and good interplay and then strong running by the backs brought an excellent try by Thaakir Abrahams (wing) converted by Chamberlain with five minutes left to play putting the visitors in a 20-19 lead, and they managed to hang in during the dying minutes to secure the valuable victory.
Dragons 19 (12) - Try: Elliott Dee. Conversion: Will Reed. Penalty goals: Reed (4).
Cell C Sharks 20 (6) - Tries: Grant Williams, Thaakir Abrahams. Conversions: Boeta Chamberlain (2). Penalty goals: Chamberlain (2).