In a highly competitive game, the Blues, who led 11-7 at half time, helped themselves to three tries from James Egan, Sam Warburton and Huw Dowden, with James Thomas adding the extras with the boot.
The only negative for the Blues was the red card shown to lock Mazin Alazawi for alledgedly stamping. Despite that numerical disadvantage or a ten minute period, the visitors held on for a crucial victory.
Cooper said, "It was a really competitive match with both sides showing how much they have improved in recent weeks.
"I am delighted for the Blues boys because they have worked so hard in the opening weeks of the season. I would like to think we can go on from here."
Jason Tovey and Ceri Young scored tries for the Dragons who put up a wonderful showing. David Langdon added a single conversion.
In the other game, the Ospreys were 6-0 winners against the Scarlets at Llandovery thanks to a penalty from wing Lee Halfpenny and a drop goal from replacement outside half Tom Cole.