Rob Henderson got their only try and although Kevin Morgan got a late try for the visitors it was the boot of Paul Burke which made the difference for Munster.
Burke and Craig Warlow had traded first half penalties with the Irishmen edging it 9-6 at the break
However soon after the restart Warlow boomed a 40-metre drop goal past the outstretched arms of Denis Leamy and Stephen Keogh to square it up.
Burke’s fourth penalty from in front of the posts pushed Munster back in front with half-an-hour remaining and two more on 64 and 67 minutes had the Dragons’ six-game run under serious threat.
Henderson then evaded a last gasp tackle from Nathan Brew to crown Munster’s victory. Burke duly converted with metronome precision to complete his 20-point haul.
But, with Munster gunning for a second try, wily Morgan sneaked away on a 60-metre breakaway to claim a try at the death.