The west Cork school looked to be heading for a comfortable victory when they led 2-6 to 0-5 with nine minutes to go.
However they were reduced to 14 men after substitute David Crowley was sent off, and this sparked a grandstand finish by the Limerick side Newcastle West will be kicking themselves.
Despite playing into the strong wind, they were camped in the Bandon half for the closing minutes but wasted three scoreable frees that might have turned the result around.
With a place in the All-Ireland series also at stake, there was an extra edge to this contest.
SMI won the toss and elected to play with the strong wind.
The sides were level twice in the opening 20 minutes and with both defences on top, there was a scarcity of scores. It didn't look good for the Limerick school when they turned over with only a two-point lead, 0-4 to 0-2.
Unlike their opponents, Bandon used the long ball to great effect in the second-half and grabbed the first of their two goals from a huge delivery by Richard Milner into Paul Coomey.
The corner-forward's first attempt was saved superbly by goalkeeper Alan Fitzpatrick, but Coomey made no mistake at the second attempt.
That goal gave the west Cork side the lead for the first time and they were not to relinquish it. A superb point from a line ball by Kevin Coffey edged Bandon further in front, and when Coomey goaled for the second time in the 45th minute, it became was very much a case of how much they would win by.
However SMI made some shrewd switches to help their recovery. Full-back Darragh Woods moved to centre-back and midfielder Timmy Stokes, a brother of Limerick senior Jason, was moved closer to goal.
Coupled with Bandon being reduced to 14 players, the switches began to work.
Using their extra man to great advantage, SMI laid siege to the Bandon goal and when wing-back Barry Downes saw his shot roll into the net off the chest of goalkeeper Eoin
McSweeney, it set the scene for a thrilling finish.
It was all hands to the pump as the Bandon side Brogans defended in the face of incessant pressure, but when Michael Quilligan missed those three frees from scoreable positions, it looked as if the West Cork side had survived.
SMI refused to give up the chase, and in those hectic closing minutes they tacked on three points in a row, while Michael Coomey took the ball off the Bandon goal line with his goalkeeper out of position.
Bandon had many heroes, but the efforts of Harry Donegan, Richard Milner, Kevin Coffey, Tomas O'Leary and two-goal hero Paul Coomey deserve special mention.
Scoil Mhuire agus Ide also had excellent players in Conor Noonan, Shawn Browne, Darragh Woods, Barry Downes and Don Hanley.
Scorers Bandon: P. Coomey 2-0; K. Coffey 0-3 (0-1 side line kick); D. Aherne (free), D. Brennan, T. O'Leary 0-1 each.
Newcastlewest: B. Downes 1-1; M. Quilligan (0-1 free), D. Hanley 0-2 each; M. Kelly, T. Condon, D. Woods 0-1 each.
HHS BANDON: E. McSweeney; M. Coomey, H. Donegan, D. McSweeney; F. Coughlan, R. Milner, R. Lehane; F. O'Connell, T. O'Leary; K. Coffey, D. Brennan, D. Aherne; P. Coomey, J. Curran, C. O'Drscoll. Sub. D. Crowley for O'Connell.
SMI: A. Fitzpatrick; F. Casey, D. Woods, M. Dowling; B. Downes, C. Noonan, S. Brown; T. Condon, T. Stokes; M. Doherty, D. Hanley, M. Kelly; M. Quilligan, K. Madigan, S. Herlihy. Subs. D. O'Sullivan for Kelly; S. Downey for O'Connell.
REFEREE: P. Lyons (Kerry).