Former Lions centre Rob Henderson scored Munster's only try as they chalked up their seventh straight Celtic League win.
Munster (9) 25
Pens: Burke 6
Pens: Warlow 2
Henderson took Mossie Lawlor's inside pass to touchdown on 69 minutes.
Dragons full-back Kevin Morgan scored a stoppage-time try but the boot of Paul Burke already had the Irish province in a commanding lead.
Ex-Harlequins fly-half Burke landed six penalties as well as converting the Henderson try.
Burke and Craig Warlow were engaged in a penalty shoot-out in the first half,
with the Munster man edging his team into a 9-6 interval lead.
The right boot of Warlow landed a 40-metre drop goal to square it up on 48 minutes.
Burke's fourth penalty from in front of the posts pushed Munster back in front
with half an hour remaining and two more on 65 and 68 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 to complete his 20-point
But, with Munster gunning for a second try, wily Morgan sneaked away on a
60-metre breakaway to claim a try at the death.
Munster are now in third in the table, level with the second-placed Dragons on 26 points.
Munster: Cullen, Lawlor, Payne, Henderson, Horgan, Burke,
Prendergast, Roche, Blaney, McIlwham, T. Hogan, Bowman, Leamy,
Replacements: Mullins for Horgan (78), M. Storey for Roche (79).
Dragons: Morgan, Wyatt, Brew, Tuipulotu, Breeze,
Warlow, Baber, Snow, Richards, Anthony, Gough, Sidoli, Ringer,
Replacements: Replacements: Bryant for Brew (76), Winn for Baber (76),
Black for Snow (62), Crawford for Richards (73),
Ireland for Sidoli (73), Beattie for Bryan (60).
Referee: Mike Hall (SRU)