Paul Turner's men crossed for tries through wingers Aled Brew and Will Harries and full-back Martyn Thomas, with 20-year-old fly-half Jason Tovey kicking the rest of the points.
Munster travelled with a strong starting line-up, boosted by captain for the night Ronan O'Gara and giant prop Tony Buckley who both lined out for Ireland against England last weekend.
The visitors were chasing a win to leapfrop the Ospreys into pole position in the table, but the Dragons, unbeaten in their last three games but winless in the league since early December, had other ideas.
Turner's side needed the victory keep their heads above the Blues and Scarlets in the race for a Heineken Cup qualification spot.
Munster enjoyed a positive start but their All Black winger Doug Howlett had a try ruled out for a knock-on and O'Gara watched his first penalty attempt bounce back off a post.
But, on 22 minutes, the Dragons took the lead. After gaining some territorial advantage, winger Brew scored a blistering try, racing 40 metres past two defenders before getting the better of full-back Paul Warwick for one of the scores of the season.
Tovey converted but the lead did not last long as the home scrum, which had been under pressure, cracked on their line to concede a penalty try that gave O'Gara a simple conversion.
The tide turned, however, when the Welsh region gained significant territory and they punished a series of Munster mistakes before half-time.
Tovey booted two penalties to give his side a 13-7 advantage at the break, with Munster losing centre Lifeimi Mafi to the sin-bin for back chat.
The Dragons used their numerical advantage for Wales Sevens international Harries to ghost over under the posts, only for that try to be erased when flanker Tommy O'Donnell got on the end of a passing movement that involved hooker Denis Fogarty, O'Gara and Warwick.
However, Munster's chances of claiming that top spot took a turn for the worse when a quick-fire attack, threaded across midfield, allowed full-back Thomas to get a third home touchdown.
The Dragons may have had the bonus point fourth try when Harries ran 70 metres from his own line but the resultant Tovey penalty in front of the posts sealed the result.
Munster, with their scrum again on top, grabbed a consolation try from Buckley but there was no denying that the Dragons were the better team on the day.
The result leaves the region just a point outside the play-off zone, in which Munster, Leinster, Glasgow Warriors and the Ospreys currently reside.
|Newport Gwent Dragons Score Card|
|Munster Rugby Score Card|