Tries from full-back Geordan Murphy and centre Ollie Smith, plus an Ian Humphreys' penalty, saw Leicester secure a 13-6 success and clinch a home quarter-final, probably against Stade Francais.
Leicester were great value for their victory in typically windy and wet conditions in south-west Ireland, and skipper Corry said: "It is an incredibly special feeling.
"We went out there and performed. Every player stood up to the challenge. Our mentality had been right throughout the week.
"It is a fantastic place to come and play rugby and I thought we showed in the first 10 minutes that we were not going to be intimidated.
"Our scrummage was fantastic, and Ian Humphreys really stepped up. Your number 10 is key to the show and he had the confidence to back himself.
"This is a huge win for us. The atmosphere in the dressing room is something special and you realise that these are the moments to savour."
Leicester's triumph ended a run of 25 successive Heineken Cup victories for Munster in Limerick on what was their last appearance at the ground before it undergoes extensive redevelopment work.
Leicester took charge from the early stages, and their win condemned Muster to second place in Pool Four and a best runners-up spot to qualify for the quarter-finals, which means they are likely to be away against Llanelli Scarlets or Biarritz.
Leicester head coach Pat Howard said: "This is the best win I've been involved with at the club. I thought our ball control was outstanding and we defended with a lot of guts."
Munster had no complaints after seeing their proud European home record come crashing down after they were out-played by Leicester's pack.
Fly-half Ronan O'Gara said: "It is obviously hugely disappointing for us but the better team won. They talked it up but they walked the walk.
"Leicester were hugely dominant up front - their pack performance was terrific - but there are two ways we can go now.
"You can just sit down or you can go away, learn the lessons and then put up a real fight. I know which option we will be taking."