Jason Hanrahan hit a last-gasp equaliser for GMIT before the students went on to win in extra-time in Newbridge.
The visitors held a one-point half-time lead, 'keeper Paul Dermody having saved a penalty from Jimmy Gelston.
Kildare later seemed to be cruising but the dismissal of Paul Divilly for a foul on Ger Mahon changed the game.
GMIT forced extra-time with three points in a row, Hanrahan's leveller coming two minutes into injury-time.
Kildare returned to 15 men for extra-time, but were soon back to 14 when Paudie Reidy picked up a second yellow.
That handed the students the initiative, and the accurate free-taking of Gelston and Hanrahan saw them home.
Scorers -- GMIT: J Gelston 0-7 (6f), K Feeney 1-0, J Hanrahan 0-3 (2f), W McNamara, C O'Donnell, D Maher 0-2 each, N Mannion 0-1. Kildare: J Enright 0-6 (6f), C Bonus 1-2, M Moloney (2f), D Harney 0-3 each, P Divilly 0-2.
GMIT -- J Keane; G O'Halloran, S Coughlan, C Forde, B Mulrooney, M Donoghue, D Maher; K Waters, J Gelston; K Greene, W McNamara, N Mannion, K Feeney, C O'Donnell, J Liddy. Subs: G Mahon for Donoghue (h-t), J Hanrahan for Greene (43); C Cannon for Feeney (56), S Kinsella for Mannion (66), F O'Grady for Cannon (67), C Cannon for O'Donnell (f-t), D McGreal for Kinsella (80), C O'Donnell for Waters (85).
Kildare -- P Dermody; P Curtin, P Reidy, J Doran, E O'Neill, R Hoban, K Divilly; K Chan, M Purcell; J Enright, P Divilly, M Moloney, T Murphy, D Harney, C Bonus. Subs: D Butler for Chan (21), N O uineacháin for K Divilly (28), A Doyle for Hoban (50), L Quinn for Harney (50), G Tynan for Bonus (70), K Divilly for Purcell (f-t), D Smith for Murphy (80), M Fitzgerald for Tynan (85).
Ref -- G Quilty (Kilkenny).