They led 10-3 at one stage in the first half, thanks to a Ben Blair penalty and conversion of Jamie Roberts' try. But then three more penalties from the immaculate boot of Munster skipper Ronan O'Gara put the Irishmen in the driving seat at 12-10 at the break.
The Blues, who are already in the Amlin Challenge Cup final against Toulon on Sunday, 23 May, were unable to breakdown the Munster defence in the second half and only grabbed victory with a 52 metre Leigh Halfpenny penalty deep into injury time.
It meant their seventh successive victory in all competitions counted for little in the end as Munster secured a semi-final clash with arch-rivals Leinster in Dublin on Saturday night.
The Blues will now be able to concentrate on their European final clash with high-flying Toulon in Marseille when they hope to become the first Welsh team to win a major Euro title.