Tom Riley and Gavin Thomas crossed for first half tries while Jason Tovey added ten points with the boot for the hosts while Munster had to settle for two Warwick penalties.
The Dragons dominated all of the early territory but could not convert the pressure into points, Tovey slicing two easy penalty attempts.
Riley got the break through the home side deserved after 20 minutes, rounding of a bulldozing run from Toby Flateau.Fresh from his duties with the Welsh national squad, Flateau powered his way upfield dragging four Munster defenders with him. Tovey sent the ball wide and a neat step from Riley sent him clear for the opening score which Tovey converted.
Former All Black Sam Tuitupou then saw yellow for a late and dangerous challenge on Tovey in the midfield.
The Dragons shunned the opportunity for a shot at goal instead Tovey sent the ball spiralling into the Munster 22.
Thomas was held up over the line after the initial surge but touchdown two minutes later from close range. Tovey added the two points.
Munster fly-half Paul Warwick then got the visitors onto the score-sheet with a penalty before his opposite number Tovey replied with three-points of his own.
The Dragons held a commanding half-time lead but it was Munster that began the second period the stronger and Warwick's early penalty brought the Irishmen a deserved three points.
Much of the half was played in the middle of the park and the only Dragons score came through a Tovey drop-goal.