Five minutes in, Williams crashed over off the base of an advancing five-metre scrum to register Munster's first try.
Although they were hampered by injuries to Murphy and Alan Quinlan, Munster pressed on and pinned the visitors back in their own half for much of the remainder.
O'Gara and Dragons replacement Shaun Connor were sent to the sin-bin 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 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.
Munster's third successive win over Welsh opposition saw them vault up to second place in the league table, level on 13 points with their fiercest rivals Leinster whom they meet in next Saturday's clash of the champions at the RDS.
|Munster Rugby Score Card|
|Newport Gwent Dragons Score Card|