Macauley Cook, Lloyd Williams and Owen Lane all crossed in the first-half purple patch to take control of the encounter.
Munster fought back through the boot of Ian Keatley and tries from Chris Cloete and Stephen Fitzgerald either side of the break but the ice cool kicking of Jarrod Evans kept the Blues out of reach.
Replacement outside half, Tyler Bleyendaal, salvaged a losing bonus point for the visitors with a last minute penalty.
Following Toyota Cheetahs loss to Glasgow Warriors on Friday night, the victory cuts the gap to third to just eight points with a trip to Zebre and then Benetton Treviso at home next.
While the Blues made a bright start a succession of penalties from South African referee, Stuart Berry, allowed Ian Keatley the opportunity to open the scoring.
Fortunately, he skewed the simple penalty wide and the Blues went on the attack after Gethin Jenkins won a trademark turnover following a well-executed exit.
They were unable to manufacture a scoring opportunity and play continued in the middle of the pitch with both sets of defence forcing errors.
However, the Blues claimed a sensational try on 18 minutes, which was started and finished by Macauley Cook.
The second-row claimed an attacking lineout and passed the ball to Ellis Jenkins on the peel. He drew Munster hooker Rhys Marshall and released Matthew Rees, who raced down the right touchline but was unable to put Lloyd Williams away.
Taufa’ao Filise and Nick Williams carried hard into the heart of the Irish province and neat play between Williams, Jenkins and Seb Davies maintained the momentum to firmly put Munster on the back foot.
And one phase later Jenkins displayed his impressive skill-set, floating a long miss-pass to Cook, who dived over.
Evans failed to add the extras but he made full amends five minutes later as he converted Williams’ individual effort.
An impressive chase from the scrum-half, Rey Lee-Lo and Aled Summerhill put Munster under pressure and Williams showed no mercy as he charged down his opposite number and namesake Duncan Williams, collecting the ball and powering over.
The Blues continued their red hot streak as they made it three tries in eight minutes to the delight of the euphoric Arms Park crowd.
This time Rey Lee-Lo was the instigator as he threaded a perfectly-weighted kick to the corner to once again unlock a Munster defence, which has conceded an average of one line-break in their last three games.
Lane showed a clean pair of heels as he out-stripped the Munster defence and beat their cover to collect the ball and dive over.
Evans kept the scoreboard ticking, making it 19-0 after just 26 minutes and it could have been more as they continued to run the visitors ragged.
They were unable to capitalise as Munster forced a key turnover and minutes later the Limerick-based outfit claimed their first try, courtesy of a driving lineout and a push in the back to propel Chris Cloete.
Keatley missed the conversion and the Blues very nearly responded with immediate effect following fine work from Jenkins, FIlise, George Earle and Seb Davies. They hammered to the Munster line but with the whitewash at their mercy they were bizarrely penalised by Berry and the score remained 19-5.
Whatever Johann van Graan said to his Munster side at the interval did the trick and they came flying out of the blocks in the second half.
They dominated the opening minutes but were matched by the Blues’ ferocious defence and settled for a soft penalty from the whistle of Berry.
Keatley cut the deficit to 11-points and his side continued to profit from the referee. Following a succession of penalties they kicked to the corner and while their driving lineout rumbled over they were held up by the good work of open side Jenkins.
Munster remained camped deep inside Cardiff Blues territory and referee Berry continued to penalise the home side with Matthew Rees sin-binned for straying offside.
Following 12 minutes of defending the pressure eventually told as the numbers ran out and Stephen Fitzgerald collected a long pass for an easy run in.
Keatley slotted the conversion to bring the visitors within four points of Cardiff Blues but they were unable to add any more during the yellow card period.
The Blues weathered the storm and after finally receiving the benefit of some decisions Evans opened their account for the second-half, making it 22-15.
Evans kept the scoreboard ticking with a fine strike on 75 minutes to stretch his side’s lead to two scores.
Bleyendaal did earn his side a losing bonus with the final kick of the game, but Danny Wilson's side took a huge step towards European qualification by securing the four points.