Ronan O'Gara kicked 14 points for his side
Munster (9) 19
Pens: O'Gara 4
Wasps (3) 3
European champions Wasps crashed out of this year's Heineken Cup after losing a fiery encounter at Thomond Park.
Four penalties from outside-half Ronan O'Gara and a late try from Denis Leamy sent Munster into the quarter-finals for the 10th season in a row.
Wasps were well short of their best and never looked like scoring a try, Danny Cipriani's penalty their sole points.
Clermont Auvergne's bonus-point victory over the Scarlets relegated Wasps to third place in the group.
The first half was tight and tense and in poor conditions free-flowing rugby was never possible.
Instead both sides had to rely on their fly-halves to kick for territory and set the platform for the forwards to attack.
And in Cipriani and O'Gara, Wasps and Munster had two men playing at the top of their games.
Any idea that the young, inexperienced Cipriani would be fazed by such an occasion were soon put to bed when the Wasps number 10 booted a 45m penalty between the posts after only four minutes.
But O'Gara responded a few moments later with both sides struggling to keep the penalty count down.
Cipriani failed with a similar effort and Wasps were left to rue that missed kick as Munster took their opportunity to take control of the game.
With the home pack adjusting better to the awful conditions, coupled with Wasps' inability to secure their own line-out, it was Munster who started to convert pressure into points.
Every match was a dog-fight and it was brilliant to be a part of it
Lock Donncha O'Callaghan in particular was a constant nuisance to the Wasps line-out, giving hooker Raphael Ibanez a torrid time.
With Leamy - for hands in a ruck - and Simon Shaw - for not retreating 10m - in the sin-bin, O'Gara sent over his second penalty for a three-point lead.
The game often spilled over with passions running high and Lawrence Dallaglio was involved in several scuffles with the Munster forwards.
Just before the break O'Gara extended the lead to six points as Wasps struggled to make any impact in the game.
Wasps' task was made all the more difficult with Shaw leaving the field with a worrying looking leg injury that stopped play for several minutes.
Shaw was later taken to hospital, leaving him a concern for England as they begin their Six Nations preparations on Monday.
The biggest cheer of the night came moments later after Dallaglio was yellow-carded for infringing at a ruck.
O'Gara punished the European champions with his fourth penalty as Munster continued to turn the screw.
Late on Munster went through 21 phases in a thrilling move that ended with Leamy going over in the corner to send the home support wild.
O'Gara added the extras to extend his haul to 14 points for the night as Munster marched on into the last eight.
Munster man-of-the-match Donncha O'Callaghan
"Today was a cup final in itself and that was how we approached it. We have huge respect for Wasps and we are thrilled to get out of the group.
"Every match was a dog-fight and it was brilliant to be a part of it. It was an immense effort.
"We would have settled for a quarter-final before the group began so not having a home tie doesn't bother us."
Wasps captain Lawrence Dallaglio
"Line-out and discipline was the key. We started well but I thought the turning point was Simon Shaw's sin-binning.
"I am not sure it was a sin-bin offence, a penalty yes, but in the context of the game, it helped them gain the momentum.
"Small decisions make a big difference but it is not sour grapes. Ultimately we were beaten by a side that played the conditions better than us."
Munster: Payne, Carney, Tipoki, Mafi, Howlett, O'Gara, Stringer, Horan, Flannery, Hayes, O'Callaghan, O'Driscoll, Leamy, Wallace, Foley.
Replacements: Sheahan for Flannery (80), Quinlan for Foley (75).
Not Used: Buckley, D. Ryan, O'Leary, Warwick, Lewis.
Sin Bin: Leamy (23).
Wasps: Lewsey, Doherty, Waters, Hoadley, Waldouck, Cipriani, Reddan, Payne, Ibanez, Vickery, Shaw, Skivington, Haskell, Rees, Dallaglio.
Replacements: Webber for Waldouck (60), Ward for Ibanez (77), Palmer for Shaw (47).
Not Used: French, Hart, McMillan, Walder.
Sin Bin: Shaw (35), Dallaglio (53).
Ref: Nigel Owens (WRFU).