It was Munster’s South African director of rugby Rassie Erasmus’ first Guinness Pro12 fixture at the Limerick venue, where they are unbeaten since last December.
Two close range scores from Murray had the hosts leading 14-7 at half-time, replying to Chris Dean’s 23rd-minute effort from his own half.
Munster replacement Conor Oliver marked his 21st birthday in midweek with a first Pro12 try, and fellow flanker Dave O’Callaghan made sure of the bonus point in the 56th minute.
With blindside Magnus Bradbury in man-of-the-match form, Edinburgh had the better of the final quarter and lively replacement John Hardie claimed a deserved consolation try.
Such was Munster’s early scrum dominance that converted prop Kevin Bryce was replaced in the fifth minute, after Tyler Bleyendaal had knocked a penalty narrowly wide.
Lock Fraser McKenzie’s shoulder charge on Jack O’Donoghue at a midfield ruck left Edinburgh temporarily down to 14 men, but the Scots proved much sharper at the breakdown in the first half.
Duncan Weir missed a long range penalty before adding a superb touchline conversion to Dean’s opportunist try. The ball squirted free from a Munster ruck and the 22-year-old winger gleefully sprinted clear from his own 10-metre line.
Munster were level within four minutes, though, as CJ Stander controlled at the back of an advancing scrum and the waiting Murray had a simple finish, with Bleyendaal converting.
Munster’s execution in open play was poor but their forwards pressed again at scrum time, driving the visitors back on their own ball and a knock-on from Sam Hidalgo-Clyne allowed his opposite number Murray to score off a Niall Scannell pass.
Oliver, who was O’Donoghue’s injury replacement, added to Munster’s lead inside 90 seconds of the restart. Bleyendaal’s inviting pass out of a tackle put the young academy back rower jinking past a flat-footed Weir for a very well-taken seven-pointer.
A series of scrum penalties resulted in Edinburgh tighthead Allan Dell being sin-binned. Weir and Cornell du Preez combined to hold up Stander off a maul, and the Munster number eight then knocked on in a second try-scoring situation.
However, a flat pass from influential fly-half Bleyendaal sent the powerful O’Callaghan through to score from the Edinburgh 22-metre line.
Hardie responded in the 66th minute, muscling over from a Hamish Watson pass, but Munster were out of reach.