They trailed 11-9 at the break and if there was a turning point it came fifteen minutes into the second half when the home side squandered a three on two that should have yielded a crucial try at a when they led by five points.
But credit Munster's defence who survived that and a subsequent assault on their line with 14 players after Tomas O'Leary owas yellow carded.
Dragons led 14-9 when replacement Denis Hurley's smashing break only ended when he was hauled down ten metres out and when Lifeimi Mafi swept the ball wide a long pass from Scott Deasy found Luke O'Dea on the wing and once again he showed his try scoring instincts diving low to score at the corner flag.
Deasy missed the difficult conversion but then booted a monster penalty and with five minutes to go Felix Jones, superb all night, snatched up a loose ball to race in under the posts for the score that sealed the outcome.
Newport Gwent Dragons: W Harris; T Chavhanga, A Tuilagi, A Smith, A Brew; L Robling, W Evans; N Williams, S Jones, N Buck, L Charteris, R Sidoli, J Groves, L Evans, T Brown. Replacements: S Parry, P Price, D way, H Ellis, D Waters, J Evans, J Dixon, S Jones.
Munster: F Jones; L O'Dea, S Tokula, L Mafi, J Murphy; I Keatley, T O'Leary; M Horan, D Fogarty, S Archer; D Foley, M O'Driscoll (capt); Dave O'Callaghan, T O'Donnell, J Coughlan. Replacements: Mike Sherry, W du Preez, BJ Botha, B Holland, P Butler, D Williams, S Deasy, Denis Hurley. Referee: C Damasco (FIR)