Irish veteran back row man Alan Quinlan wrapped up Munster's win with a late score and the defeat leaves the Dragons 13 points behind the Scarlets in seventh place in the race for automatic qualification for the Heineken Cup, but with two games in hand.
Wales Under-20s head coach Edwards had made an impressive start since taking temporary charge of the Dragons with four wins and draw from his first five games following the departure of Paul Turner.
The Dragons, who included fit-again Wales squad member Toby Faletau, led 9-6 after a hat-trick of penalties by Tovey despite losing Ashley Smith and Robert Sidoli to injury. But Howlett turned the game with two tries before half-time.
Tovey and wing Adam Hughes combined to hand hooker Jones an easy score as the Dragons hit back just two minutes after the break. But Munster, with several Ireland internationals to call-upon, broke free in the final 20 minutes as Mick O'Driscoll, Murphy and Quinlan crossed to settle the game and keep the Irish province nine points clear of reigning champions in the Ospreys in the hunt for a top two finish to clinch a home Play-Off semi-final.