Munster effectively ended the Dragons' hopes of progressing past the Heineken Cup group stages with a dominant display at Newport's Rodney Parade.
HEINEKEN CUP POOL ONE
Dragons (3) 8
Munster (17) 24
Tries: Leamy, Horan
Pens: O'Gara (2)
Drop-goals: Lawler, O'Gara
Denis Leamy's short-range try gave the Irish a 17-3 half-time lead after a drop-goal apiece from Mossie Lawler and Ronan O'Gara, who added two penalties.
Marcus Horan was driven over from a lineout after the break as the Dragons pack proved no match for the visitors.
Gareth Chapman's injury-time try for the Dragons counted for nothing.
It was the home side's only attacking move of note as the backs finally combined in a sweeping move from left to right.
Flanker Jamie Ringer delivered the decisive pass which gave winger Chapman enough space to cross in the right corner.
But the score took none of the gloss off Munster's win, which takes them above Castres to second place behind Sale in Pool One.
Despite establishing a number of promising attacking situations in the first half, Munster's first try came when there seemed little danger for the Dragons.
The home side should have cleared their lines from a scrum inside their own 22, but the superior Munster pack forced a turnover and flanker Leamy stretched over from a ruck just short of the tryline.
The Irish had dominated possession up to that point, and aggressive play at the breakdown forced turnovers on the rare occasions the Dragons strung some phases together.
With such an advantage at the halfway stage, Munster barely reached third gear after the break.
O'Gara's accurate kicks kept the Dragons penned into their own half, and it was from the fly-half's boot that Munster scored their second try.
Dragons winger Richard Fussell had little choice but to run into touch with the ball yards from the left corner, and a textbook catch and drive from the resulting lineout sent prop Horan over.
O'Gara's first successful conversion took Munster 19 points clear and there was no way back for the toothless Dragons.
Dragons coach Paul Turner:
"On a positive note we stuck at it and the fact that I had to play three club players in the back three and they all came good augurs well for the future.
"Munster have got one of the best line-outs in Europe and our execution let us down, it sometimes happens like that.
"But I feel we're growing and we're moving on. We've got a double-header against Munster now and then our bread and butter against the three other Welsh regions, but I'm not despondent."
Munster coach Declan Kidney:
"We're not disappointed, we didn't come here for the bonus point we came to win, sometimes you play into opposition hands by playing loose.
"The Dragons showed in the last few minutes that you couldn't give them space and it was out of respect for them that we played as we did.
"They will have some players back next week and they'll have learned from this. They'll be stronger when they come over to play us in the return."
Dragons: A. Thomas; Chapman, Tuipulotu, Sweeney, Fussell; Warlow, Cooper; Black, S. Jones, R. Thomas, Gough, Sidoli, Hall, Ringer, Owen.
Replacements: Brown, Maddocks, Robinson, Charteris, Bryan, Bryant, Baber.
Munster: Lawlor, Connolly, Kelly, Halstead, Horgan, O'Gara, Stringer, Horan, Flannery, Hayes, O'Callaghan, O'Driscoll, Leamy, Wallace, Foley.
Replacements: Roche, Fogarty, Hogan, S. Keogh, O'Leary, Manning, B. Murphy.
Referee: Tony Spreadbury (RFU).