Edinburgh moved within two points of Pro14 Conference B leaders Munster with their first away win over the depleted province in five years.
Eroni Sau scored the decisive try in a nail-biting contest, gathering a fine Blair Kinghorn kick on 63 minutes.
Matt Scott had given Edinburgh an early lead, but Tommy O'Donnell powered over to tie the match at half-time.
Ben Healy, 20, on his first Pro14 start, then slammed over two penalties, but Sau's try proved the winning score.
Edinburgh leapfrog Scarlets, who were well-beaten 29-5 by Ulster in Belfast on Friday night, and are two points behind the Scottish team in third place.
Despite missing 10 members of Ireland's Rugby World Cup squad, and fielding a side showing 14 changes from Saturday's European Champions Cup draw with Racing 92, Munster earn a losing bonus point.
These sides have thrown up some compelling and ferocious battles in recent times. Frustratingly for Edinburgh in the two most important meetings - last season's Champions Cup quarter-final at Murrayfield and the Pro14 play-off in Limerick the season before - Irish experience prevailed in tight matches.
In contrast to the hosts, Richard Cockerill named a strong Edinburgh team, with Stuart McInally and Hamish Watson getting their first action since representing Scotland in Japan.
The visitors made the perfect start when Scott crashed into the midfield from a 5m scrum and while he initially looked to have been stopped short, he wriggled close enough to the line to reach out and score.
Jaco van der Walt's conversion and subsequent penalty established a 10-0 lead, though Healy clawed three back for the home side from the tee.
Without so many front-liners, Munster's play lacked cohesion but as the first half moved towards its conclusion the Irish side started banging at the door. Edinburgh withstood around 20 phases of intense pressure on their own line, but their heroic defence was in vain as O'Donnell eventually burrowed over.
Healy converted to level things up and his penalty early in the second half edged Munster ahead for the first time.
McInally, out of form and dropped from his role as captain to the bench in Scotland's final World Cup match, showed his extended break may have done him some good with a powerful thrust through the heart of the Munster defence. He had front-row partner Pierre Schoeman in support but the rampaging South African was hauled down inches short.
Healy struck again with the boot to make it 16 unanswered points for the men in red until substitute Simon Hickey stopped the Edinburgh bleeding with a penalty of his own.
The visitors were awarded a penalty which may have been just about inside Hickey's range, but instead they went to the corner and the gamble paid off.
Playing off penalty advantage from the subsequent line-out, Kinghorn dinked a beautiful chip over the defence for Sau to collect and score.
With 17 minutes to protect a two-point lead, Edinburgh showed some street-smarts and steel to see it out and claim a victory that takes them within two points of Munster at the top of Conference B.
Munster: Daly; Nash, Arnold, Goggin, Wootton; Healy, McCarthy; O'Connor, Marshall, Archer, Wycherley, O'Shea, O'Donoghue (capt), O'Donnell, Botha.
Replacements: O'Byrne, J Cronin, Knox, Holloway, Oliver, N Cronin, Hanrahan, R Scannell.
Edinburgh: Kinghorn; Sau, Bennett, Scott, Van der Merwe; Van der Walt, Pyrgos; Schoeman, McInally, Ceccarelli, Toolis, Gilchrist, Bradbury, Watson, Mata.
Replacements: Willemse, Sutherland, Berghan, Carmichael, Miller, Shiel, Hickey, Taylor.