They opned brightly yet failed to register a score and when the home side raced into a 16 point lead Munster looked to be on the ropes.
However, just before the break Ian Dowling got over in the corner and this score and whatever was said at half-time had the desired effect.
Billy Holland closed the gap further with a try from close range and three Paul Warwick penalties put Munster in front before Warwick sealed the outcome with a try under the posts in injury time.
Munster: S Payne; I Dowling, K Lewis (R Tipoki.56 min), L Mafi, A Horgan; P Warwick, T O'Leary; Darragh Hurley, D Fogarty, F Pucciariello; M Melbourne, M O'Driscoll; B Holland (J Coughlan 50 min), N Ronan, A Foley capt. Replacements (not used): S Cronin, T Ryan, T O'Donnell, G Hurley, J Manning,
Newport-Gwent Dragons: Martyn Thomas, Gareth Wyatt, Rhodri Gomer-Davies, Ashley Smith (G Maule), Richard Mustoe, Aled Thomas, Andrew Williams(W Evans), Hugh Gustafson (A Black), Steve Jones (B Daly), Rhys Thomas, Luke Charteris, Andrew Hall (P Sidoli), Dan Lydiate ( J Ringer), Richard Parks, Joe Bearman (N Fitisemanu).