Edinburgh (3) 13
Tries: Visser Cons: Paterson Pens: Paterson 2
Munster (6) 16
Tries: O'Callaghan Con: O'Gara Pens: Warwick 2, O'Gara
Visser scored with a breakaway try for Edinburgh at Murrayfield
Munster made it two wins from two Magners League games against a disappointing Edinburgh side who slumped to consecutive defeats.
Two penalties from Paul Warwick to one by Chris Paterson on the stroke of half-time saw a dominant Munster side only lead 6-3 at the interval.
Tim Visser's converted try five minutes after the break put Edinburgh ahead.
But Donncha O'Callaghan replied with a converted try and although Paterson levelled O'Gara's kick secured victory.
The Scots were under the cosh from the outset against a powerful Munster outfit that piled on the pressure and were denied a try in the opening 40 minutes by a solid home defence.
Edinburgh were forced into defence for much of the match
Edinburgh had hardly been out of their own half when Warwick slotted a simple penalty to put Munster ahead and he almost had another soon after when the home side were penalised at the scrum, but this time his kick drifted wide.
The first half was marred by a 20-minute stoppage for a serious injury to Edinburgh's Argentine lock Esteban Lozada and, on his eventual departure, things immediately got worse as Alex Grove was adjudged offside and Warwick potted penalty number two.
Edinburgh almost nicked a try from a retreating Munster scrum that coughed up the ball, but too often they were turned over or gave away the penalty.
In the final minute of the half, a 38-yard penalty was at the limit of Paterson's range, but it dropped over via the post, leaving Munster wondering how they could have had so much pressure and territory to go in only three points ahead.
Edinburgh got just the start they needed to the second half to boost their confidence - a Phil Godman kick plucked out of Doug Howlett's arms by Visser for the Dutch winger to sprint 40 yards for the first try of the night.
Paterson added the extras, but from there on Munster's power ensured that they were on the front foot.
Ian Dowling scorched in off his wing following Tomas O'Leary's 56th-minute break and was hauled down a metre short.
However, O'Callaghan, who had been on the pitch for around 60 seconds, powered over.
O'Gara slotted the conversion and, although Paterson's 62nd-minute penalty tied the scores, there was an inevitability about the Munster belief that they would prevail.
And O'Gara duly landed the penalty that put them in the lead with 13 minutes remaining, with the Irish team successfully running down the clock to grind out what could be an invaluable win on the road.
Edinburgh coach Rob Moffat:
"It was a poor performance by us. That is what happens if you don't look after the ball.
"It is amazing that we were still in the game when we took the lead, but we weren't aggressive enough in contact and paid the price."
Munster captain Denis Leamy:
"Although we had all the first-half pressure, we never really threatened and we had to show a lot of character when we went behind.
"Murrayfield has not been a good ground for us in recent years, so we are delighted to have got the win."
Edinburgh: Paterson; Robertson, Cairns, Grove, Visser; Godman, M Blair; Jacobsen, Ford, G Cross, Lozada, MacLeod, Newlands, Talei, Rennie.
Replacements: Houston for Grove (52), D. Blair for Godman (65), Traynor for Jacobsen (56), Kelly for Ford (65), MacKenzie for Lozada (30), McInally for Talei (64). Not Used: Gilding, Laidlaw.
Munster: Jones; Howlett, J Murphy, Tuitupou, Dowling, Warwick; Stringer, Du Preez; Varley, Buckley, D Ryan, O'Driscoll, Quinlan, Ronan, Leamy.
Replacements: O'Gara for Warwick (32), O'Leary for Stringer (50), Horan for du Preez (55), Fogarty for Varley (62), Hayes for Buckley (44), O'Callaghan for O'Driscoll (55), O'Mahony for Quinlan (67). Not Used: Barnes.
Ref: James Jones (WRFU).