With both sides missing 11 players, attacking chances were few as the Blues' Lee Thomas and Munster's Paul Burke shared six first-half penalties.
Burke added two more kicks, then Jeremy Manning extended the lead with another.
Munster held out when prop Federico Pucciariello was sin-binned. Late on, Marc Stcherbina's fine converted try for the Blues set up an exciting end.
The capital side could not follow it up, though, and had to be content with a losing bonus point.
Blues (9) 16
Con: L Thomas
Pens: L Thomas (3)
Munster (9) 18
Pens: Burke (5), Manning
Warren, R. Williams, J. Robinson, Stcherbina, Morgan, L. Thomas, R. Powell, M. Jones, G. Williams, B. Evans, D. Jones, Goode, Schubert, Molitika, A. Powell.
Replacements: Dewdney for Warren (67), Quinnell for Goode (62), Lewis for Molitika (86). Not Used: Llewellyn, Goodfield, W. Evans, Davies.
Manning, Kelly, Connolly, Halstead, Pitout, Burke, O'Leary, Roche, Flannery, Pucciariello, Hogan, O'Driscoll, O'Sullivan, Wallace, S. Keogh.
Replacements: Payne for Burke (56). Not Used: Buckley, Fogarty, S. O'Connor, J. O'Connor, Prendergast, B. Murphy.