Rockwell survived 10 minutes of nervous second-half stoppage-time to book a home quarter-final with CBC in Clanwilliam.
Leading 13-0 with just 12 minutes of regulation time left, the home side survived a stirring fightback from St Munchin's.
After a scrappy opening, the Rockwell scrum began to dominate, and this led to a Billy Johnston penalty giving the Tipperary school a 3-0 lead after a quarter of an hour.
Just two minutes later they extended that lead to eight when No 8 Mikey Wilson finished an overlap in the left corner.
Johnston struck his difficult conversion well, but it drifted narrowly wide; his side still enjoyed a deserved 8-0 advantage, which they carried into half-time.
Rockwell were still on top early in the second half, and when full-back Stephen Quirke finished off a glorious counter-attack to put them 13-0 ahead, it looked to be curtains for Munchin's.
But a quadruple substitution from the Limerick side brought fresh energy to the attack, and in the 49th minute, replacement Kieran McGuirk crossed the line to give them hope.
Jason Kiely's conversion left six points between the sides.
That gap was reduced to just three with eight minutes left with a Kiely penalty, but the "first try" rule meant that a draw would not have been enough for Munchin's to progress.
They dominated the lengthy period of injury-time, but several knock-ons in the Rockwell '22' proved crucial, and the Tipp side clung on to claim the victory.
Rockwell – S Quirke; C Manton, L Molloy, B Ryder, T Brennan (K Moynihan 32); B Johnston, D Egan (K Looby 60); N Campion (C Beary 60), B Murray, J Tierney; J Binchy, C Cashman; J Kennedy, D Fehily (L Devereaux 32), M Wilson.
St Munchin's – J O'Hanlon; C Stephenson, M Lyons (J Stone 43), S Kelly, M Browne; J Kiely, B Bennett (E O'Connor 43); E O'Callaghan, J Burke, R Kirwin (K McGuirk 43); S Hayes, C Radcliffe (H McDonald 43); A Moloney (E Quinlivan 58), A McNamara, J Foley.
Ref – A Brace (MAR)