Ronan O'Mahony 1 Try
CJ Stander 1 Try
Declan Cusack 1 Penalty
Stander's late try was vital as it denied Plymouth the all-important losing bonus-point.
Munster A started well and nearly scored a try in the opening minute through debutant Alex Wootton but the winger was halted with a high tackle.
Johnny Holland kicked the penalty into the corner and Peter Malone's side kept the visitors pinned in their own '22 with Holland eventually making the pressure tell with a penalty in the fifth minute to make it 3-0.
The visitors responded immediately and Dan Mugford kicked his first penalty of the night to make it 3-3 and the out-halves traded further penalties for a 6-6 scoreline after 17 minutes.
Munster A retook the lead after 23 minutes when Ronan O'Mahony touched down in the left corner. Dave O'Callaghan and CJ Stander made the hard yards before the ball was flung wide and, after some great hands, Ronan O'Mahony blasted over for the first try, his fourth in four B&I Cup games this season.
Johnny Holland split the posts with a superb conversion to make it 13-3 and that's how it stayed until the break.
The second half was a scrappy affair with neither side able to get any real rhythm going in their game.
Johnny Holland kicked the first points of the half after 46 minutes to make it 16-6 but the gap was reduced to seven by former Munster out-half Declan Cusack, a first half substitute, when he kicked his first penalty.
Despite being within reach on the scoreboard, Plymouth were unable to force any sustained pressure on the Munster line and South African Stander crossed in the final minutes to seal the win.
The try came from a Munster five-metre scrum, Stander made a break from the base of the scrum and, with the support of the pack, the no.8 went over in the left corner to put Munster A out of reach.
Johnny Holland added the extras to complete the scoring in a deserved 23-9 Munster A win.
Young Munster centre Dan Goggin came on late in the game for his first Munster A appearance.
Munster A: Ronan O'Mahony; Alex Wootton, Cian Bohane, Niall Kenneally (Dan Goggin 75), Darren Sweetnam; Johnny Holland, Gerry Hurley (Brian Haugh 79); Alan Cotter (Brian Scott 40), Niall Scannell (Capt), John Ryan; Ian Nagle, Billy Holland; Dave O'Callaghan (Shane Buckley 77), Barry O'Mahony, CJ Stander. Replacements: Max Abbott, Brian Scott, Darren O'Shea, Shane Buckley, Brian Haugh, Dan Goggin, Rory Scannell
Plymouth Albion: Ben Woods; Lewis Warner, Heath Stevens, Pale Nonu, Jamie Davies; Dan Mugford, Ruairi Cushion; Tom Harrison, Max Crumpton, Lloyd Fairbrother; Dan Williams, Romana Graham; Herbie Stupple, Sam Matavesi, Rhys Oakley (Capt.). Replacements: Gareth Evans, Ben Rogers, Dave Morton, Rob Langley, Declan Cusack, Toby Howley-Berridge, Chris Elder.