The conditions were perfect for running rugby, as both teams showed intent to attack from kick off.
The Blues raced into a 12-0 lead at a bitterly cold BT Sport Cardiff Arms Park but errors kept Bristol in the game as they claimed three tries against the run of play.
But Matthew Morgan proved the difference against his former side as he claimed a brace after the break before putting Sam Warburton away.
The Blues made a decent start to the encounter with Rey Lee-Lo and particularly Nick Williams carrying to good effect.
Bristol also displayed their attacking intent and Adrian Jarvis had the first opportunity to put points on the board but the fly-half fired a simple penalty wide.
Both sides failed to take opportunities during an opening quarter littered with mistakes, but the Blues surged into the lead on 22 minutes.
Shingler kicked a pair of penalties to the corner and despite some strong defence from the visitors, the pressure eventually told as Dacey crashed over.
Shingler missed the conversion but he was back at the tee two minutes later after Anscombe picked off Nick Koster’s pass to race under the sticks from 70 metres.
This time Shingler made no mistake to stretch the Blues’ lead to 12-0 after 24 minutes.
Alarm bells were ringing when Tusi Pisi intercepted Matthew Morgan’s pass but thankfully referee Mike Adamson was playing advantage and Shinger bisected the posts.
Bristol responded on 31 minutes after the ball cruelly bounced away from Lloyd Williams, allowing Andy Uren to put Jordan Williams over unopposed. Jarvis converted to make it 15-7.
Bristol added a second try on 39 minutes as Williams intercepted Shingler’s pass and hacked through. The ball bounced favourably again and the wing released Jack Tovey.
Jarvis was again on target to cut Cardiff Blues’ lead to 15-14 at the break.
The Blues came storming out of the blocks in the second-half with Alex Cuthbert a rampaging presence on the wing.
He showed a devastating combination of pace and power as he bumped off two defenders but Bristol just about clung on.
However Wilson’s men remained in the ascendant and they claimed a third try on 43 minutes.
Following some good carries up the middle the ball was worked right and quick hands from Anscombe and Shingler released Morgan.
He has one defender to beat and with Cuthbert on his outside he dummied his way past Luke Arscott for a crucial try.
The Blues piled on the pressure following the score, with Cuthbert at the fore, but they were dealt a major blow on 56 minutes.
On the second occasion in close succession a try appeared inevitable but Lee-Lo’s flicked pass was intercepted by Williams, who raced the length of the pitch for a second try.
Jarvis converted to give his side the lead for the first time but it lasted a matter of minutes with Shingler nailing a penalty from the touchline.
The Blues burst into life again as the final quarter approached with Blaine Scully driving through a defender to make an unlikely break.
He managed to hold off the defender long enough to find Shingler in support and he released Tomos Williams.
The replacement scrum-half tore into Bristol territory but was eventually caught by Jordan Williams.
Max Compton was sent to the sin-bin after interfering at the breakdown as the Blues failed to convert the opportunity.
But Morgan struck for a stunning individual effort on the counter-attack to secure the try-scoring bonus-point.
Shingler converted to stretch his side’s lead to 30-21.
The game kept opening up, which suited Morgan perfectly, as he made yet another stunning break before finding captain Sam Warburton on his inside, who saw off the final defender to slide in for Cardiff Blues’ fifth try of the afternoon.