It was the Blues' first win on Munster soil since October 2007 and occurred on a night when Ronan O'Gara became the Irish province's most-capped player.
O'Gara will not want to remember his 233rd competitive appearance as he was outshone by his opposite number, man-of-the-match Rhys Patchell.
The 19-year-old Patchell converted both tries, adding to an early penalty, and displayed a calmness and control beyond his years in the number 10 channel.
O'Gara kicked a penalty in each half but Munster lacked penetration throughout and have now fallen to sixth in the RaboDirect PRO12 standings.
Connacht put away a disappointing Newport-Gwent Dragons side 30-11 at the Sportsground as they halted a run of four straight RaboDirect PRO12 defeats.
Although they failed to garner a likely bonus point in the final quarter, a penalty try and efforts from George Naoupu and Danie Poolman had already confirmed the Irish province's dominance.
Connacht fly-half Dan Parks stamped his mark on a scrappy game with a 15-point contribution, while replacement Jonathan Evans scored a late consolation try for the Dragons to add to Tom Prydie's brace of penalties.