Charlie Hore opened the scoring with a penalty and they added to their tally with a try from prop Tommy McGee straight from the re-start.
The Blues' big name signing Jonah Lomu triggered the opportunity by spilling the ball when under no pressure. The home side capitalised immediately with hooker Ross Ford playing a key role.
In the end it was lock Scott MacLeod who unselfishly off-loaded to McGee for the easy score.
Hore cemented his side's advantage by slotting home the extras.
The visitors rallied with a penalty of their own from the boot of Nick MacLeod but Hore restored the 10-point cushion with his second penalty and added a third before the end of the half.
The Blues refused to roll over and kept the game alive as a contest after the interval with two more successful penalties from MacLeod but struggled to find greater reward thanks to a resilient Reivers defence.
To add to the Blues' woes they conceded a second try soon after with Nikki Walker benefitting from some good work by Simon Danielli and Stuart Moffatt.
Hore converted before adding yet another penalty to put the game seemingly beyond the Blues' reach.
But they rallied once more and a try from centre Marc Stcherbina, converted by Macleod, gave them some hope.
Then in stoppage time veteran Craig Quinnell grabbed another try, which again MacLeod converted, but in the end it proved to be not enough.
|Border Reivers Score Card|
|Cardiff Blues Score Card|