Munster led 9-3 at half time thanks to three Ronan O'Gara penalties and the tries left them 19-3 to the good as the game entered the final quarter.
By that stage Munster were without O'Gara and Rob Henderson both forced to retire injured and Leinster did reduce the deficit with two David Holwell penalties before Eric Miller's 76th minute try - converted by Holwell - set up a tense finish.
In the end the late Leinster flourish only earned them a bonus point - It was more than they deserved after been out-thought and out-fought by the men in red.
Toyota Man of The Match - Paul O'Connell
Munster: C Cullen; S Payne, M Mullins, R Henderson (M Lawlor), A Horgan; R O'Gara (P Burke), P Stringer; M Horan, F Sheahan, J Hayes; D O'Callaghan, P O'Connell; A Quinlan, D Leamy, A Foley (J Williams).
Leinster: G Dempsey; S Horgan, G D'Arcy, D Hickie; D Holwell, G Easterby; R Corrigan, S Byrne, E Byrne; L Cullen, M O'Kelly; E Miller, S Jennings, V Costello.
Referee - Alan Lewis.