Dragons fly-half Jason Tovey missed a last-minute penalty attempt as a young Dragons side missed out on a losing bonus point.
It was the Welsh visitors who made the better start though, with Steffan Jones thumping over a huge penalty ten minutes in to give Darren Edwards' side the lead.
But it did not last long as new signing Ian Keatley knocked over three points of his own to bring the scores level.
And Munster's class soon told as Murphy made a scintillating break before offloading to centre Danny Barnes to score the night's opening try, Keatley adding the conversion to make the score 10-3.
With four minutes to go before half-time Munster grabbed their second try after a fantastic move off a lineout put Lifiemi Mafi over to stretch the lead to 17-3 with Keatley's conversion.
Tovey brought the Dragons back to 17-6 at the break, but they soon had to cope with being a man down as Ben Castle received a yellow card two minutes into the second half.
But Munster failed to make the Welsh side pay, Keatley missing a penalty before Mafi received a yellow card for Munster's persistent infringing.
Tovey edged the visitors closer with another penalty as captain Peter O'Mahony became the second Munster player to be sent to the bin.
And the champions' indiscipline continued as hooker Damien Varley also received his marching orders, Tovey knocking over the resulting penalty to bring the Dragons back to within five points.
But Keatley denied them the bonus point with a penalty six minutes from time, before Tovey's long-range effort with the last kick of the game fell well short.
|Munster Rugby Score Card|
|Newport Gwent Dragons Score Card|