Head coach Danny Wilson demanded his side responded following last week’s derby defeat to the Ospreys and they did so emphatically at Ashton Gate.
Despite trailing to an early Max Crumpton try, the Blues went into half-time with a healthy eight-point lead thanks to the boot of Gareth Anscombe and tries from Rey Lee-Lo and Josh Turnbull.
Alex Cuthbert kept the scoreboard ticking with his second try of the season and following a frustrating spell, before Tom James wrapped up a maximum points haul.
The Blues were slow out of the blocks as Bristol dominatied the opening exchanges. They created a scoring opportunity after less than four minutes with Adrian Jarvis combining with Thretton Palamo to release Tom Varndell but thankfully Matthew Morgan did enough to force a foot into touch.
However referee Pascal Gauzere was playing advantage and Jarvis knocked over a simple penalty for a 3-0 lead.
From the Blues first venture into territory Anscombe levelled the scores. First he kicked a long penalty to the corner and after Bristol were pinged at the maul, he made it all square.
But Bristol remained lively with Rhodri Williams breaking through and grubbering ahead for a foot-race with second-row Jarrad Hoeata.
Matthew Morgan came across to take the ball into touch but Bristol rumbled over from the resulting lineout with Max Crumpton the scorer and Jarvis converting.
Wales’ Capital Region responding with some fine carries and offloading from the pack which laid the foundations for Anscombe to successfully strike a second penalty.
And just two minutes later he added a third following a thunderous carry from Alex Cuthbert and good work from Nick Williams and Morgan.
Bristol were unfortunate not to respond after a scintillating David Lemi break. They forced their way over the whitewash but were unable to ground the ball and Gauzere came back and sent Matthew Morgan to the sin-bin for a high tackle.
Following last week’s yellow card period, which saw Cardiff Blues ship 19-points, alarm bells may have rung.
But the Blues responded emphatically and struck almost instantly the after Tomos Williams capitalised on a fortunate bounce. He was unable to beat the defence but Wilson’s men were soon awarded a penalty which was kicked to the corner.
They failed to drive over but from the next phase Anscombe dinked the ball over Bristol’s aggressive defence and Lee-Lo collected to score beneath the posts.
Anscombe converted and Cardiff Blues claimed a second try while down to 14-men after Nick Koster was also shown yellow.
The ball was dinked to the corner and this time they set up the driving lineout successfully, allowing Turnbull to peel off down the blindside to score. Anscombe was unable to add the extras but the try had given his side a 21-13 lead at the interval.
In the second-half the Blues flexed their forward muscle at scrum-time, with Rhys Gill particularly destructive.
They won three scrum penalties in the opening five minutes and while Williams was unable to power over from the back, the ball was recycled and following a succession of phases Cuthbert was bundled over.
Anscombe added the simple extras and the visitors were in the hunt for a bonus-point try.
They were frustrated for large periods of the second-half but it looked as though a ghostly Steve Shingler break would provide the fourth. He beat several defenders but failed to find the support.
However they had a second bite of the cherry after being awarded a penalty and after kicking to the corner and launching another driving lineout, the ball was worked back to the left for James to cross for his fifth try of the season.
Bristol crossed over for a consolation try in the final play of the game, with Joe Joyce powering over.