Stranded at the foot of the RaboDirect Pro12 with just one win from five games, the capital side started strongly, sagged in the second half, but came roaring back with Tim Visser's late try to win an enthralling match.
The 29-23 scoreline, with both sides swapping the lead, was strongly reminiscent of the 2011/12 run which took Michael Bradley's side to the Heineken Cup semi-finals. Since then it has been largely all downhill for Edinburgh, but new coach Alan Solomons was given huge encouragement by the manner in which his side persevered against Munster in front of 7000 supporters.
While it was hard to accept his assertion that this was another gradual improvement - more like a giant leap - Solomons said: "If you analyse the footage there has been improvement every week and today we managed to cross the line.
"I am a big believer that the line between success and failure is the finest in the world. If you persevere you will cross it."
Just like two seasons ago, the boot of captain Greig Laidlaw was a huge factor. Starting the day on 487 points for Edinburgh, he crossed the 500 threshold before half-time.
The home side also got a huge boost from the performance of Scotland centre Matt Scott, who scored the first try and had a fine match in his first start of the season.
"Matt busted the line a few times," said Solomons. "He's a really good player. This was only his second game [the first was as a replacement] since the South Africa tour in the summer. There is a lot more to come from him.
"It was great for all the guys that they got that result. It is a real boost for their confidence.
"As a side we need to be performance focused as opposed to outcome focused because one will follow the other. We have been telling the players they are so close to getting there."
Solomons had a problem getting into the stadium after forgetting his pass, but once a spectator had assured a steward the unidentified man was indeed the Edinburgh coach it turned into a great afternoon for the South African and his players.
Scott had already made a couple of half breaks before he touched down in the fifth minute.
The ball came along the line to the left and the Scotland centre powered over the line. Laidlaw converted off a post to make the score 7-0.
It got better for the home side when Munster were penalised for going over the ball six minutes later. Laidlaw stepped up to add three points to the score.
The lead was cut when Ian Keatley took advantage of an infringement by Grant Gilchrist to peg back the score to 10-3 and the penalty sparked off Munster's best spell of the first half.
A Laidlaw kick was charged down by Donnacha Ryan, and although the forward couldn't keep his feet after collecting the ball there was plenty of support which allowed Casey Laulala to touch down and Keatley converted to level the scoreline. Although Laidlaw notched another penalty after Keith Earls had been penalised for holding on to the ball, the visitors continued to enjoy superiority in this midway spell.
The home side conceded a free kick following a scrum infringement and that led to Munster hooker Mike Sherry scoring the try which put his side ahead for the first time. Keatley again added the conversion.
Another Laidlaw penalty reduced the arrears to 16-17, before adding a fourth before the interval as his side regained the lead.
Twelve minutes into the second half Munster were back in front, again from a Keatley penalty, and this time the visitors kept their foot on the pedal.
The stand-off extended the advantage to four points with just over 15 minutes remaining, but it was a poor reflection of their second-half superiority.
It was also fatal because Edinburgh regained the lead with a disputed converted try. Grant Gilchrist collected replacement JJ Hanrahan's kick and fed the deadly Visser who had just enough space to find a passage down the right touchline.
Edinburgh were made to wait a long time for the score to be confirmed as the video referee decided whether Scott had deliberately blocked Hanrahan when he kicked the ball forward. The decision went the home side's way and Laidlaw converted.
Worse followed for Munster when Laidlaw added his fifth penalty of the game to put his side six points ahead.
He then hit the crossbar with another attempt just 40 seconds from the end and a truly exciting spectacle ended with Munster trying fruitlessly to run in the converted try they needed.
Edinburgh: J Cuthbert; D Fife, N De Luca, M Scott; T Visser; H Leonard, G Laidlaw (capt); A Dickinson (W Blaauw 68), R Ford, W Nel (G Cross 68), G Gilchrist, S Cox, D Basilaia (R Grant 61), C Du Preez, D Denton
Munster: F Jones (J Hanrahan 67); K Earls (D Hurley 61), C Laulala, J Downey, S Zebo (D Williams 72); I Keatley, C Murray; D Kilcoyne (J Cronin 53), M Sherry (D Varley 58), S Archer (BJ Botha 53), D Ryan, P O'Connell (capt), P Butler (C Stander 53), N Ronan (D O'Callaghan 65), J Coughlan
Referee: JP Doyle (RFU)