A Nick Williams hat-trick helped the Magners League champions to victory at Musgrave Park on Sunday.
Ronan O'Gara kicked over the first points five minutes from the break but James Arlidge replied for the Dragons to make it 3-3 at half-time.
Williams crashed over for his first try on 45 minutes as Munster took a firm grip on the game.
The number eight went over again and Doug Howlett added the third before Williams completed his treble.
Springbok centre Jean de Villiers made his debut for Munster in front of the Cork supporters.
A stomach bug prevented Keith Earls from taking his place for Munster, meaning positional switches for Felix Jones and Barry Murphy and a late promotion from the bench for de Villiers.
Lions duo O'Gara and Donncha O'Callaghan also made their first starts of the season.
Munster started well, de Villiers winning a penalty on halfway and then setting up his centre partner Lifeimi Mafi for a jinking run into the 22.
The Dragons gradually gained territory and turned down a kick at goal before Munster, with a strong defensive scrum, were able to force a turnover and clear the danger.
Jones, Mafi and Denis Hurley saw plenty of possession in the first quarter but Munster grew frustrated by the Dragons' well-organised, aggressive defence and O'Gara had to react sharply to prevent Ashley Smith from releasing a team-mate for the line.
Turner & Scrum V on Dragons loss
O'Gara missed his first shot at the posts but the deadlock was finally broken five minutes before half-time when he split the posts after a scrum infringement by Nigel Hall.
Arlidge hit back with a penalty of his own and was narrowly wide with an injury-time drop-goal attempt following a terrific midfield break by Joe Bearman.
Yet the Dragons lost their way in the second half as Tony McGahan's men upped the intensity.
Five minutes in, New Zealander Williams crashed over off the base of an advancing five-metre scrum to register Munster's first try.
Having lost Murphy and Alan Quinlan to injuries, Munster pressed on and pinned the visitors back in their own half for much of the remainder.
O'Gara and Dragons replacement Shaun Connor saw yellow for a bout of fisticuffs at a ruck close to the Welsh side's line and just moments later, Williams used his brute strength to barge past Harris and Martyn and Thomas for his second touchdown.
Scrum-half Tomas O'Leary added the conversion and did likewise after replacement Howlett speared through a gap and outpaced Aled Brew to score behind the posts.
The Dragons tried valiantly to mount a comeback but Munster sewed up the bonus point eight minutes from the end when Williams took a quick tap and bulldozed his way over again from close range.
Dragons coach Paul Turner: "We had a couple of opportunities in the first half and turned round at 3-3, but if you don't take those chances they come back to haunt you.
"It was nip-and-tuck until the break, but they probably had too much field position and they are clinical when they get the chance.
"Nothing went for us in the second half. There were a couple of 50-50 calls that didn't go our way and that was the game gone."
Munster: Jones, Murphy, de Villiers, Mafi, D. Hurley, O'Gara, O'Leary, Horan, Fogarty, Buckley, O'Driscoll, O'Callaghan, Quinlan, O'Donnell, N. Williams. Replacements: Howlett for Murphy (8), Manning for O'Gara (74), Morland for O'Leary (66), Varley for Fogarty (60), Ryan for Quinlan (30), Coughlan for O'Donnell (60). Not Used: Brugnaut.
Dragons: M. Thomas, Brew, Riley, Smith, Fussell, Arlidge, W. Evans, Gustafson, S. Jones, Hall, A. Jones, Sidoli, Lydiate, Harris, Bearman. Replacements: Robinson for Gustafson (56), Goodfield for S. Jones (56), McKenzie for Hall (56), MacDonald for Sidoli (58), Webb for Lydiate (68). Not Used: Connor, Lee.
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