The victory sees the Blues move up to third in the RaboDirect Pro 12 points table.
The Dragons had the better of the early stages but they were unable to convert pressure in to points. Cuthbert made them pay in the 19th minute when he popped up outside Casey Lualala to cross over. Leigh Halfpenny converted to give the Blues a 7-0 lead.
Halfpenny increased the lead with a penalty before Jason Tovey pegged back three points with a well struck penalty.
On the stroke of halftime Brad Davies put further daylight between the two sides when he powered over to give Halfpenny an easy conversion. Leading 17-3 at the break, the Blues were in full control.
The Blues brought on Jamie Roberts at the break in place of Dafydd Hewitt but he took a bang to his knee early on in the second half. He struggled on but eventually departed the clash in obvious pain to give Wales an injury scare six weeks before the start of the 2012 Six Nations.
Halfpenny and Tovey continued to trade penalties before Cuthbert showed his lethal finishing prowess in the 72nd minute to score his second try of the evevning and send the Dragons crashing to defeat.
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