Tomas Quinlan gave Constitution an early advantage with a first minute penalty from 20 metres, but almost from the kick off, Lansdowne attacked, and a rash tackle on the right wing gave referee Paul Haycock little choice but to award a penalty try.
Conor McKeown made no mistake in the conversion from in front of the posts but Quinlan kept Constitution in the game with a second penalty in the 10th minute. McKeown restored Lansdowne's half time advantage to 10-6 with his second penalty in the 39th minute.
McKeown and Quinlan continued to exchange penalties in the ten minutes after the interval, to leave the Dubliners with a 13-9 lead entering the final quarter.
The decisive score came in the 70th minute, when a strong attack on the Lansdowne line ended with centre Conor Cunningham claiming a vital touch down from a clever kick to the line by Quinlan, who added the points from in front of the posts.
Throughout, Constitution's defence was sound and they saw out the final minutes to claim a famous victory.
Cork Con Team:
C.McAuliffe; G.Ryan, C.Cunningham, L.O'Connell, D.O'Sullivan; T.Quinlan, R.Foley; A.Slattery,M.Abbott, M.McTighe; G.Mullins, D.Moloney; D.Hurley, S.Dwyer, E.Beehinor. Replacements: M.O'Sullivan, S.Galvin, M.Coughlan, R.O'Halloran, J.Murphy, K.Clancy, A.Dorgan (all played).
I.Fitzpatrick; C.Ryan, S.Coughlan, R.B.Kearney, J.McCormack; C.McKeown, D.Henry; C.Ganly, S.Delahunt, O.Hefferan; S.Gardiner Capt.,R.Catlin; R.Tyrell, S.Keelan, J.O'Neill. Replacements: J.McKenna, E.Moffitt, J.O'Shea, R.Trayer, B.Ridgeway, W.Lappin, G.Molloy.