Steve Jones touched down for the Dragons, but tries from man-of-the-match Mick O'Driscoll, Johne Murphy and Alan Quinlan made certain of the bonus point for Munster.
The result also completed a clean sweep of victories for the Irish provinces over the weekend, with Munster and Leinster holding play-off positions, Ulster close behind and Connacht in an improved position of eighth.
Munster and the Dragons both showed an eagerness to attack but early penalties prevented any momentum being built up as Warwick and Tovey traded blows.
Warwick nudged Munster ahead before Tovey struck an upright with his first penalty. He made amends in the eighth minute before Warwick kicked Munster back in front.
Tovey then moved the Dragons 9-6 ahead with two well-struck efforts as the likes of Joe Bearman and Toby Faletau made the hard yards.
The visitors had to realign their backs division before kick-off. An injury to Will Harries saw Pat Leach move to full-back with Ashley Smith brought into midfield.
Smith picked up a knock midway through the first half, bringing Rhodri Gomer-Davies into the fray, and the Dragons' bad luck continued when lock Rob Sidoli fell awkwardly in a tackle and injured his elbow.
Munster were the better team in the second quarter, with Simon Zebo and Lifeimi Mafi starting to pose a threat.
Munster turned down a close range kick in favour of a scrum in the 28th minute. After a solid set piece and and carry from Denis Leamy, James Coughlan's crafty backhanded offload took two Dragons defenders out and sent Howlett in at the right corner.
Warwick converted from the touchline and Munster closed out the half with another try from Howlett, who used Murphy as a foil to nip between two covering players and make the line. It was the New Zealander's fifth try in four league games.
The Dragons made a terrific start to the second half, putting their captain Jones over for a try within two minutes. Faletau and Tom Riley made good incisions before Adam Hughes was sprung through a gap on the right and Jones was up in support to finish off in the corner.
The increasingly influential Warwick landed a penalty to steady Munster at 21-14 and young scrum half Conor Murray, who impressed on his first start, passed for O'Driscoll to rumble over for the hosts' third try.
A Tovey penalty reduced the Dragons' arrears to nine points entering the final quarter, but Munster, with their bench players making an impact, had more in the tank.
Full-back Murphy glided inside Hughes and Tovey for a converted try eight minutes from time, and an overthrown Dragons' lineout, five metres from their line, allowed Quinlan to close out the scoring.
|Munster Rugby Score Card|
|Newport Gwent Dragons Score Card|