Dragons made a strong start and took the lead when Jacob Botica slotted a penalty from 30 metres out after good work at the breakdown by James Benjamin.
Munster took the lead when home captain Fineen Wycherley crashed over and Ben Healy added the extras.
Loosehead prop Jeremy Loughman added a second shortly after for Munster before Dragons hit back with Wellington exploiting a gap to score under the posts. Botica’s kick reduced the home lead to 14-10 at the break.
Both sides showed good defensive resolve after the interval before Munster scored a third try through scrum half John Poland on the hour.
Two long range penalties from Healy extended the advantage before a yellow card to Greggains saw Munster go all out for the try bonus point.
Calvin Nash duly added the crucial fourth try with two minutes to go before the Dragons had the final saw when Greggains went over with the final play.
Dragons A: Carwyn Penny, Will Talbot-Davies, Calvin Wellington, James Benjamin, Deon Smith, Jacob Botica, Dafydd Buckland; Gerard Ellis, Rhys Lawrence, Chris Coleman, Joe Davies, Huw Taylor, James Thomas, Lennon Greggains (c), Taine Basham
Replacements: Zac Hewlett, Scott Evans, Luke Yendle, Max Williams, Ben Fry, Rhodri Davies, Tom Hoppe, George Gasson
Munster A: Stephen Fitzgerald; Alex Wootton, Matt More, Alex McHenry, Calvin Nash; Ben Healy, John Poland; Jeremy Loughman, Billy Scannell, Ciaran Parker; Fineen Wyhcerley (Capt), Sean O’Connor; Jack Daly, John Hodnett, Gavin Coombes.
Replacements: Eoghan Clarke, Cronan Gleeson, Keynan Knox, Paddy Kelly, Darragh O’Grady, Charlie O’Doherty, Jake Flannery, Sean French.
