The sides were level a goal apiece at the end of 90 minutes and Bonner then produced a moment of magic with three minutes of extra-time remaining, stroking home the winner.
Stiofáin Naofa had the better of the opening half and the evergreen Danny Murphy up front was a constant threat, an early free kick testing Carlow keeper Darren McGarry. Carlow eventually found their rhythm and Dean Broaders and Bonner went close before the break.
But it was the Cork side who might have taken the lead, Michael O’Regan shaving the post after Murphy set him up. The deadlock was finally broken on 73 minutes when sub Andy Mulligan was taken down in the box by David King and Broaders beat Stiofain Naofa keeper Eoghan Daly from the penalty spot. King picked up his second yellow card and was sent off.
Carlow looked on their way to clinching the win until Murphy fired in a free kick in the closing minutes and Mady Noah Cisse touched home the equaliser.
Extra-time was a tight affair and with three minutes left, Bonner linked up with Ryan Delaney to teer the winner past a helpless Daly.
D McGarrry; E Dempsey, R Delaney, S Last, G O’Boyle; A McAlavey, S Dunne, J Bonner, A O’Rourke, K McDaid; D Broaders.
A Mulligan (for O’Rourke 71 mins), T Croke (for McDaid 100 mins), C Poole for McAlavey 100 mins), J Morgan (for Broaders 108 mins), D McGuinness, U Ivkovic, S Manley.
E Daly; D Kirby, K McNamara, K Holland, M Cisse, R Coughlan, N Kennedy, S Caulfield, R Kenny, D Murphy, M O’Regan.
J Cott (for Kennedy h-t), G Corcoran (for O’Regan 100 mins) I Matiki, D Dondolo, C O’Hanlon, B O’Callaghan, I Matiki, S Ward.
P Tuite (Dublin).