Glasgow advanced to a November 14 semi-final and will learn who they play after Edinburgh's match with Cardiff at Meadowbank today. Ulster and Connacht are also in the last four along with Glasgow.
Glasgow got off to the worst possible start, conceding a try after just four minutes when Munster prop Simon Kerr, went over for a try unchallenged after a drive and ruck on the Glasgow five metre line. Munster almost added to their lead but strong and, at times, desperate Glasgow defence kept them out despite having had Gareth Maclure sin-binned.
Great kicking from Dan Parks saw Glasgow settle and following a bout of pressure they deservedly scored with Rory Kerr powering over to touch down. Dan Parks added the conversion and a further penalty to send Glasgow in at half-time, with a 10-7 lead.
Things got even better for Glasgow after the break when good work by Kenny Sinclair saw No.8 Paul Dearlove power over for his first try of the season. Dan Parks missed with the conversion but he made up for it with a difficult penalty attempt from wide on the right to make the score 18-7.
Munster fought back and following the awarding of a penalty for deliberate off-side, scrum-half Eoin Reddan put centre Mike Mullins in on the right.
With just four points between the teams Munster put Glasgow under heavy pressure but strong tackling, secure set-piece and the long, relieving kicks of Dan Parks saw Glasgow hold on for a superb victory.
Glasgow coach Hugh Campbell said: "That was a fantastic result for Scottish rugby. Munster are a quality side but we showed we could match them in every aspect.
"No one let their heads go down when Munster went ahead and the most pleasing thing is there was no loss of focus at any stage.
"People might think it will be difficult to top this sort of result and performance but there's more to come from this group of players."
A great display from Dan Parks won him the man of the match award but there were heroic displays from every Glasgow player.