The Men of Gwent lead 14-9 with 15 minutes to go thanks to the boot of Lewis Robling and an Ashley Smith try.
But Ian Keatley ensured Munster stayed in touch and the Irish Province produced a ruthless snatch and grab with tries from Luke O’Dea and Felix Jones to secure their first win in Newport since 2009.
Keatley opened the scoring for the reigning PRO12 champions within two minutes of the kick-off at Rodney Parade but Lewis Robling, making his first regional start at fly-half, hit-back with a shot of his own.
The Dragons surged into the lead thanks to a scintillating break which Smith neatly finished.
Former Springbok Tonderai Chavhanga produced the opening and released Will Harries. The full-back raced down the left wing and stepped passed Felix Jones, before cutting inside and firing a long pass for Smith to crash over.
Robling failed to slot the relatively simple conversion and was punished for his inaccuracy with Keatley adding quick-fire penalties.
But he made amends with a penalty for the Dragons to enter the interval leading 11-9.
Robling broke a second-half deadlock on 64-minutes to stretch the hosts’ lead to five-points but Munster stormed back.
Munster levelled the scores thanks to an O’Dea try on 67 minutes. A Denis Hurly burst made the initial inroads, the ball was recycled and Scott Deasy fired a pin-point miss pass to O’Dea to squeeze in the corner.
Deasy failed to add the extras but made amends on 72 minutes with a penalty to snatch the lead.
And Jones pounced on a loose Lewis Evans pass in the final minutes to put the result beyond doubt, with Deasy converting.
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