Tries from Andrew Conway, Andrew Goodman, James Tracy and Fionn Carr in addition to 10 points from the boot of Noel Reid helped them to a 30-26 victory.
Munster won both interprovincial 'A' team games between the sides this season and beat their rivals 36-29 at the RDS in last year's semi-final.
It took a try from winger Ronan O'Mahony deep into stoppage time against Cornish Pirates for Munster to set up the all-Ireland tie and keep their interest in the competition alive. In winning 10-9, Munster exacted revenge for their loss to the Pirates in the 2010 inaugural B&I Cup final.
The following day Bedford Blues take on Newcastle Falcons in an all-English affair at Goldington Road.
British & Irish Cup semi-finals:
Munster 'A' v Leinster 'A', Friday April 26, KO: 7.30pm
Bedford Blues vs Newcastle Falcons, Saturday April 27, KO: 3pm