In their final home game of the season, it was a much-needed morale booster for the Scots.
Two heavy defeats on the bounce had seen them freefall from top-spot to ninth. But this victory sees them leap-frog Munster and move up to eighth.
But they lost captain Todd Blackadder with a hand injury and centre Tom Philip with a knee problem to take some of the gloss off the win.
Munster went into attack from the opening whistle and rocked Edinburgh when they took the lead with an early penalty by Conrad O’Sullivan.
This stung the home side into action. Inspired by a try-saving tackle by Hugo Southwell on Martin McPhail, they levelled with a long-range Brendan Laney kick after Munster were penalised at a ruck.
The Scotland reject grabbed the lead in identical fashion before Andy Dall claimed the crucial opening try following a well-controlled maul.
Laney managed another penalty from a wide angle. But with Derrick Lee in the sin bin, Munster clawed back three points thanks to O’Sullivan before the break.
Edinburgh found themselves under heavy pressure after the restart; yet they added to their advantage when, following a Munster knock-on, a herd of pacy players raced up field. Marcus Di Rollo and Simon Webster combined to send Ally Hogg cruising in under the posts to give Laney an easy conversion, and put the game beyond doubt.
O’Sullivan reduced the deficit with his third penalty, but Edinburgh held out for the win.