It was the first time this season that Edinburgh tasted defeat at home in the Celtic League and although Chris Paterson had the opportunity to snatch victory deep in injury time it was a victory that Munster richly deserved.
They lead 13-7 at half-time thanks to a superb Trevor Halstead try converted by Ronan O'Gara, who added two penalties.
Their second half try came from John Kelly and although basic errors allowed the Gunners back into contention Munster defended quite heroically to eek out a huge morale boosting win ahead of their trip to France next weekend.
Shaun Payne; John Kelly (Tomas O'Leary), Barry Murphy, Trevor Halstead, Ian Dowling; Ronan O'Gara, Peter Stringer; Federico Pucciariello, Jerry Flannery (Denis Fogarty), John Hayes (Eugene McGovern), Donncha O'Callaghan, Paul O'Connell capt; Stephen Keogh, David Wallace, Mick O'Driscoll (Trevor Hogan).
Hugo Southwell; Chris Paterson capt, Marcus Di Rollo, Peter Jorgensen, Francisco Leonelli; Phil Godman, Mike Blair; Dave Hewett, Dougie Hall, Craig Smith; Alastair Kellock, Scott Murray;Allister Hogg, Simon Cross, Simon Taylor.