Munster were on the mark early when Jeremy Manning landed a penalty from the Leinster ten metre line but his opposite number Ian Keatley leveled after Munster were penalised for not rolling away at a ruck.
With the home side being the more inventive the reward came after James Coughlan and Barry O'Mahony combined down the left to send Mossy Lawlor clear and when he was bundled in touch, Munster stole the lineout, went wide and Murphy had too much space and class for the Leinster defence.
That lead was extended ten minutes later after Keith Earls showed delightful step to shred the Leinster defence and Murphy was on his shoulder to run in unopposed.
Leinster attempted to go wide off a lineout on the Munster 22 but Murphy's crunching tackle on Felix Jones ended that move only for Munster to be penalised and Keatley reduced the deficit with his second successful penalty.
In injury time, Leinster had no answer to a fluid Munster rolling maul and Barry O'Mahony scored their third try for a 16 point interval lead.
Munster totally dominated the opening stages of the second half and Mossy Lawlor looked certain to score under the posts stopped short by a Fionn Carr ankle tap. Minutes later it was Earls who looked odds on to score but he knocked on Billy Holland's pass and those lost opportunities looked particularly costly when Leinster established themselves in Munster's 22 and left it after Jamie Hagen crashed over to the right of the posts (22-11).
Boosted by that score Leinster dominated territorially but had neither the guile nor the gusto to breach the Munster defence and when the home side lifted the siege, Coughlan crowned a good afternoon's work with that late try.
Munster A: Mossie Lawlor (Tom Gleeson 60 min); Keith Earls, Barry Murphy, Conan Doyle, Ciaran O'Boyle; Jeremy Manning (Evan Ryan 60 mn), Duncan Williams (Gerry Hurley 70 min); Dave Ryan (Gary Walsh), Denis Fogarty (Mike Essex 52 min), Tim Ryan (Daragh Hurley 64 min); Mark Melbourne, Dave Sherry; Billy Holland (Tommy O'Donnell 51 min)), Barry O'Mahony, James Coughlan capt.
Leinster A: Fionn Carr; Shane Monahan, Felix Jones, Michael Berne, Vasily Artemiev; Ian Keatley, Paul O'Donoghue; Ruaidhri Murphy, Richie Sweeney, Paul Doran Jones; Richie Leyden, Ben Nagle; Stuart Abbott, Sean O'Brien capt, Kevin Sheahan. Replacements: Jamie Hagan, Gavin O'Meara, Niall Smullen, Brian Moroney, James Power, Kyle Tonetti, Kevin McKenzie.