And it seemed the home side were set fair for the final when tries from Luke McGrath and Dominic Ryan had them leading 20-9.
But Munster struck back with a brace from Luke O'Dea and one for Barry O'Mahony to regain the lead
Deasy missed an added time penalty but then landed his seventh successful kick in extra time before adding the conversion to Dave Kilcoyne's try to seal the outcome.
Munster:S Scanlon Cork; L O'Dea, D Barnes, JJ Hanrahan, I Dineen; S Deasy, D Williams : D Kilcoyne, S Henry, J Ryan, B Hayes, I Nagle; B Holland, capt, B O'Mahony, P Butler. Replacements: D Fogarty, P Borlase, P Donnelly, B O'Hara, C Sheridan, D Cusack, R O'Mahony.
Leinster:D Kearney; A Conway, B Macken, C O'Shea, F Carr; N Reid, L McGrath; J McGrath, A Dundon, M Moore; D Browne, M Flanagan; R Ruddock capt, D Ryan, L Auva'a. Replacements: T Sexton, J O'Connell, J Coughlan, J Murphy, M healy, C Marsh, A Boyle