Following three devastating defeats at the death, the Blues were fired up from the very first whistle and tore into Munster.
Nick Williams set an early precedent before the home side wobbled as Munster snatched two fortuitous tries.
But John Mulvihill’s men regained their composure with Halaholo the centre of attention. He created a stunning try from Tomos Williams before half-time and claimed one of his own after the break.
Anscombe kept the scoreboard ticking with his flawless haul and with minutes remaining scrum-half Williams put the icing on the cake as he sniped over for the bonus-point try.
It appeared as though the Blues had made a perfect start when Owen Lane crossed after just two minutes.
Mulvihill’s men won their own kick-off, thanks to some fine aerial work from Jason Harries, and embarked upon a sustained period of pressure. They hammered at Munster’s defensive line and breached it when Willis Halaholo flicked an inside pass to Owen Lane at pace.
But after protestations from Peter O’Mahony, referee Quinton Immelmann reversed his call and went to the TMO, eventually adjudging Rey Lee-Lo to have blocked.
Munster cleared from the ensuing penalty but Cardiff Blues soon asserted their scrum dominance, earning an opportunity to kick to the corner.
They again stretched the visitors with Williams eventually powering over the whitewash for a well-deserved try.
Anscombe added the simple extras but Munster quickly responded with two dubious tries, against the run of play, which left the Arms Park crowd incensed.
First, following what appeared to be a hand in the ruck, Munster broke on the counter from inside their own half with Andrew Conway chipping ahead and collecting to score.
Two minutes later they broke out of their half once more and despite a support line that could have been deemed blocking and a pass that appeared forward, Conway crossed for a second. Carbery missed both conversions but Munster were now leading 10-7.
The quick-fire points were a devastating blow to the Blues, who could have been left shell-shocked, but they responded in perfect fashion.
From a lineout on the half-way line Cardiff Blues struck with Halaholo carving the Munster defence apart with a devastating step.
He raced towards JJ Hanrahan and demonstrated his deadly foot-work once again, leaving the full-back looking for his ankles as Tomos Williams finished.
Anscombe converted to stretch his side’s lead to 14-10 before Carbery struck with a long-range penalty.
The Blues should have claimed a third try soon after, following a fine chip and collect to from Anscombe.
He managed to release Tomos Williams with a fine offload but Kristian Dacey was unable to hang onto the scrum-half’s audacious pass with the try-line at his mercy.
The score remained 14-13 at the interval but after just six minutes of the second-half Halaholo turned to scorer from provider.
The opportunity came from a monster touch-finder from an Anscombe penalty. First the forwards set a driving lineout but the ball was released quickly and at first phase Halaholo eased around Jaco Taute for a stunning solo try.
Anscombe kept the scoreboard ticking with the conversion and a long-range penalty to make it 24-13.
Munster responded with their typical bloody-mindedness and attempted to grind Wales’ Capital Region down.
Following a pair of penalties kicked to the corner the Limerick-based outfit went through countless phases as thy bludgeoned their way to the whitewash.
At one stage it appeared ominous for Cardiff Blues but scarred by recent weeks they grew in every collision, eventually forcing a penalty thanks to Kristian Dacey.
Anscombe soon cleared and following a Tomos Williams charge down, they were in the Munster half.
Williams showed good patience not to fly in on the ball and forced a mistake. From the ensuing scrum, Dmitri Arhip flexed his muscle to earn a penalty and Anscombe duly bisected the uprights.
Despite the 14-point advantage there was still a nervous air at the Arms Park but the Blues kept their foot on the peddle and with 10 minutes remaining Anscombe, who had been imperious all evening, landed another long-range effort.
With time running out, Cardiff Blues went all guns blazing for the maximum points, and it paid off as Williams sniped over for his second of the evening.
Wales' Capital Region will host Toyota Cheetahs next week at the Arms Park, as they look to carry momentum into their third home game of the campaign.