Exeter made a commanding start to the encounter with the likes of Dave Ewers carrying to good effect and Gareth Steenson pulling the strings.
But the first real chance fell to Cory Allen who half intercepted Steenson's pass but left the ball behind.
The Chiefs worked their way back down field and launched a sustained period of pressure with ferocious ball carrying resulting in Johnson eventually powering over.
Steenson missed the conversion and Cardiff quickly cut the deficit through the boot of Halfpenny.
But Exeter continued to dominate the territorial battle and Steenson made amends for his earlier miss to bring the scores to 8-3.
And the hosts stretched their lead when Mumm burst through a ruck and cantered home on 24 minutes, with Steenson adding the extras.
It took just two minutes for them to kick the scoreboard back into action. Phil Dollman made the initial inroads and Jess eventually raced clear, with Steenson again converting.
And they wrapped up the bonus-point and virtually sealed the result as Vainikolo cut inside Cuthbert.
Steenson converted to bring the scores to 29-3 on the half hour mark but there was still time for Exeter to notch up a fifth, with White powering over against his former team.
And the Chiefs fly-half dissected the posts to hand his side an emphatic 36-3 lead at the interval.
The Devon club claimed a sixth try shortly after 50 minutes with the superb Steenson sending Ian Whitten over.
Williams and Copeland claimed quick-fire tries to give the Welsh region a glimmer of hope and Exeter were dealt a double blow with Whitten and Sireli Naqelevuki sent to the sin-bin in quick succession.
The Blues capitalised on their numerical advantage as Cuthbert squeezed in the corner and Robinson salvaged a try-scoring bonus-point in the closing stages.