Blindside Christian Dacey bagged the first try with No.8 Lewis Mills, full-back James Loxton and wing Joe Xiberras adding the rest. Joe Deacon kicked two conversions to round off another comfortable evening for the high-flying Blues.
The Dragons, who bagged a point against the Scarlets at Stradey Park last time out, trailed 17-3 at half time - David Langdon kicking a penalty - but rallied after half time with Langdon adding a second penalty and Danny Ellis converting a try from flanker Gareth Patterson.
In the end, however, they were second best and remain at the foot of the table with one point from three games.
Blues high performance manager Gafyn Cooper said: "We made some changes after half time and lost a little fluency, but we are pleased with all 22 boys.
'They played well despite a concerted effort from the Dragons in the second half."
Meanwhile, the Ospreys, who have had an indifferent start to the season, defeated the Scarlets 54-21 scoring seven tries to boot.
Centre Ashley Beck helped himself to a brace as did No.8 Rory Pitman and Kristian Phillips. Anthony Buselli added the seventh, with half-back partner Daniel Biggar converting five tries and adding three penalties for a 19-point haul.
Ieuan Davies and Matthew Lemon scored tries for the Scarlets, with Daniel Newton adding a conversion and Daniel Etteridge two penalties and a drop goal.
The Ospreys under-20s were also celebrating a victory this week - they defeated the Dragons 13-7 on Tuesday night