Danny Wilson’s men took a deserved 16-13 lead into the interval thanks to Turnbull and the pin-point accuracy of Jarrod Evans.
However, two Munster tries in the space of three minutes at Thomond Park proved decisive and the Blues were unable to battle back as the hosts put the game to bed as former Arms Park favourite Robin Copeland wrapped up the bonus-point.
The Blues made an assured start in Limerick with Evans and Willis Halaholo pinning Munster back with sublime touch-finders to the corner flag.
Munster secured the ball and cleared on both occasions but they were unable to exit their half and Evans soon opened the scoring after the hosts strayed offside.
The hosts however, showed plenty of promise with the ball in hand and slick hands from their backline saw them threaten but the Blues hung on and the ball was lost.
Cardiff Blues were penalised at the ensuing scrum and while Niall Scannell overthrew, the visitors were unable to clear effectively.
Wilson’s side were instantly put under pressure with Alex Wootton charging down the left and following a series of phases Conor Murray, one of three British & Irish Lions returning to the Munster XV, darted over from the base.
Ian Keatley converted and to make matters worse Jack Roberts was forced off little more than 10 minutes into his competitive debut.
Evans kept his side in touch with a well-struck penalty, from distance, on 20 minutes and they soon struck for their opening try.
The opportunity arose from a strike play. Shingler looked to find Halaholo with a long, flat-pass and although the ball missed the centre it fell into the path of Rhun Williams.
He found Tom James, who beat one man but was stopped agonisingly short of the line but possession was maintained and Turnbull crossed in the opposite corner.
Evans added the extras from the touchline to give his side a 13-7 lead after 24 minutes and he traded further penalties with Keatley.
The Munster fly-half edged his side closer as both sides struggled to get to grips with South African referee Quinton Immelman’s interpretation at the breakdown.
And Cardiff Blues had their backs to the wall after they conceded another penalty at the contact area with Keatley kicking to the corner.
However, Munster were unable to cross, despite a strong power game, with the ball lost over the line and the Blues able to clear for a 16-13 half-time lead.
Rassie Erasmus’ side piled on the pressure early in the second-half with a succession of scrum penalties, which eventually saw Taufa’ao Filise sin-binned.
While some of the early decisions appeared harsh, once Immelman had pinged the Blues for a fifth occasion it appeared ominous. However, at the next set-piece it was Munster who conceded a free-kick and Evans cleared.
But the Irish province came roaring back and John Ryan stepped inside the defence to dive over with Keatley converting.
To compound the Blues woes, Munster displayed a ruthless edge and claimed a second try in the space of three minutes with Rory Scannell tearing through the midfield and finding JJ Hanrahan in support.
Keatley maintained his 100 per cent record to bring the scores to 27-16 after 55 minutes.
As the hour-mark passed the encounter opened up and both sides displayed their attacking prowess with Tomos Williams, Matthew Morgan and Tom James almost combining to compete a fine try.
But it was Munster that finished their chances with another midfield bust laying the platform for Murray to tear down the right with Copeland diving over, securing their bonus point.
Keatley, showing his playmaking abilities, released Hanrahan for his second and Munster's fifth try of the afternoon.
Blaine Scully, James and replacement Lloyd Williams came close to scoring a consolation try in the closing stages of the game but Munster held out for the 23 point victory.