Paul O'Connell returned to action as a second-half substitute as Munster ran in two tries to defeat the Dragons convincingly at Musgrave Park.
A James Cronin try and eight points from the boot of JJ Hanrahan helped the hosts to a 13-6 half-time advantage.
Kris Burton kicked two penalties and added another at the start of the second half to reduce the arrears.
Munster skipper Peter O'Mahony touched down for the second try, Hanrahan converting and kicking another penalty.
The victory for the Irish province sees them move up to third in the Pro12 standings, two points behind Glasgow and the Ospreys.
The Dragons lie seventh, level on points with the sixth-placed Scarlets after four rounds of matches.
Introduced by Munster for the closing 30 minutes, O'Connell was playing for the first time since fracturing his right forearm during the Lions' opening Test against Australia in June.
The second row was closely watched from the stands by new Ireland head coach Joe Schmidt and forwards coach John Plumtree as Munster bounced back from losing in Treviso last weekend.
Prop Cronin's second try of the season moved the home side clear after Burton had matched Hanrahan's early brace of penalties.
Yellow cards for Dragons captain Andrew Coombs and Jevon Groves left the Welsh region in all sorts of trouble and Munster skipper O'Mahony's close-range touchdown, supplemented by the further points from Hanrahan, made the game safe.
The Dragons, who opened their campaign with two wins from three, were level at 6-6 by the end of the opening quarter in Cork without having achieved much in attack.
O'Mahony and his back-row colleague Paddy Butler were the guilty parties as Burton cancelled out Hanrahan's lead scores, the former Ireland Under-20 star having landed penalties after seven and 19 minutes.
Hanrahan missed a tricky third attempt from the left wing and as the Dragons' well-organised defence continued to frustrate Munster, Burton was off target with a snap drop goal effort.
A knock-on from a lineout maul, allied to a scrum infringement from John Ryan, prevented Munster from creating pressure in the Dragons' 22, but O'Mahony swooped on Hugh Gustafson's overthrown lineout to set his side up for a telling 35th-minute attack.
Direct running from Ivan Dineen punctured the visitors' defence and with Cathal Sheridan delivering quickly from the base of rucks, Cronin came on the charge to bulldoze through a tackle and make the try-line.
As the rain began to fall, Hanrahan fired over the conversion from the left to establish a seven-point advantage and give Munster something to build on.
Burton clawed back three points early in the second half, slamming over a penalty from just inside the Munster half, but the Dragons lost the services of Coombs shortly afterwards.
The Dragons skipper was sin-binned for a reckless use of the boot on Damien Varley as he attempted to clear a ruck and just a minute later, flanker Groves followed him for collapsing an advancing Munster maul.
The 13 men could not hold out and O'Mahony wormed his way over from a close-in ruck, with confirmation from TMO Jude Quinn, and Hanrahan's successful conversion making it 20-9.
O'Connell came on to huge acclaim from the home crowd, joining fellow stalwart Donncha O'Callaghan in the second row, as the province tried to push on for a bonus point.
But Dragons replacement Sam Parry won a crucial penalty as his side defended close to their line, and it was the Welshmen who had the better scoring chances in the closing stages.
Munster were forced to defend for much of the remainder, with Dan Evans and Ross Wardle both crowded out in the right corner as the Dragons hunted for their own bonus point.
Their best opportunity was spoiled by a Wardle knock on as replacement Jason Tovey looked set to put him over late on.
Munster: Johne Murphy; Andrew Conway, Keith Earls, Ivan Dineen, Simon Zebo; JJ Hanrahan, Cathal Sheridan; James Cronin, Damien Varley, John Ryan; Donncha O'Callaghan, Dave Foley; Peter O'Mahony (capt), Sean Dougall, Paddy Butler.
Replacements: Mike Sherry for Varley (68), David Kilcoyne for Cronin (61), Stephen Archer for J Ryan (61), Paul O'Connell for D Foley (56), CJ Stander for Butler (70), Duncan Williams for Sheridan (70), Ian Keatley for Murphy (74), Felix Jones for Hanrahan (64).
Dragons: Dan Evans; Matthew Pewtner, Ross Wardle, Jack Dixon, Tom Prydie; Kris Burton, Jonathan Evans; Phil Price, Hugh Gustafson, Francisco Chaparro, Andrew Coombs (capt), Matthew Screech, Jevon Groves, Lewis Evans, Netani Talei.
Replacements: Sam Parry for Gustafson (61), Owen Evans for Price (52), Dan Way for Chaparro (52), Rob Sidoli for Screech (67), Ieuan Jones for Groves (58), Richie Rees for J Evans (60), Jason Tovey for Burton (70), Adam Hughes for Prydie (67).
Sin Bin: Coombs (50), Groves (50)
Referee: Neil Paterson (Scotland)
Assistant referees: Sean Gallagher, Gary Glennon (both IRFU)
Citing commissioner: Peter Ferguson (IRFU)
TMO: Jude Quinn (IRFU)