Munster's lead at the top of the table was reduced to three points after Leinster beat Connacht on Saturday night with Ulster moving back into the top four.
It was a nightmare start for Rob Penney's side as they found themselves 20 points down after 37 minutes but an Ivan Dineen try on the stroke of half-time gave them hope.
Two further tries in the second half from Dave Kilcoyne and James Coughlan - both from rolling mauls - brought Munster to within four of the hosts but two late Ruan Pienaar penalties sealed the win for Mark Anscombe's side and denied the visitors a losing bonus point.
Munster will be on Heineken Cup duty for the next two weekends as they face Gloucester at Kingsholm this Saturday with Edinburgh visiting Thomond Park on Sunday week at 12:45pm with tickets available here.
Munster A are in action at St. Mary's this Friday with Peter Malone's side hosting Nottingham in a must-win British and Irish Cup clash at 7:30pm. Adult tickets are available here and for more information click here.