A late Jeremy Staunton kick broke Edinburgh hearts after the home side had bravely fought back to level the Celtic League match at Myreside in front of a crowd of over 5,000.
Edinburgh were finally sparked into life in the 45th minute after a Jason Holland drop-goal had given the Irish side the upper hand.
Edinburgh then got into the game and Duncan Hodge kicked another penalty before their try finally arrived.
The ball squirted out when the scrum was disrupted on the Munster line and Simon Taylor was first to it, crossing the line to the delight of the home crowd. Replacement Gordon Ross converted.
Ross kicked a penalty to tie the game with four minutes left, time enough for Munster to break upfield and Staunton to kick the winner.
Munster deservedly lead 19-9 at half-time thanks to a fine try by flanker David Wallace after centre Mike Mullins had shredded the home defence.
Full-back Staunton converted from touch and apart from an early horror shot he kicked well to put over four penalties.
Edinburgh contributed to their first-half difficulties with a series of errors, particularly giving away possession on their own throw-ins.
The only player looking likely to raise the team performance was full-back Chris Paterson, but he was too far from the action.
On the stroke of half-time Duncan Hodge, who had kicked his three penalties without trouble, put the ball into the corner from a penalty but nothing came of it and Munster broke up-field for their final first half score, a penalty from Staunton.
EDINBURGH: C Paterson; C Murray, M di Rollo, C Howarth, CSharman; D Hodge, G Burns; A Jacobsen, S Scott; C Smith, A Dall R Metcalfe, M Leslie S Taylor
MUNSTER: J Staunton; D Crotty, M Mullins, J Kelly, A Horgan; J Holland, P Stringer; P Clohessy, F Sheahan, J Hayes, M Galwey, M O'Driscoll, A Quinlan, D Wallace, A Foley
Referee: N Williams (WRU)
New Zealand full back Christian Cullen made a successful return from knee surgery by scoring two tries and setting up another in Wellington's 35-17 win over Taranaki yesterday.
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