The Letterkenny side drew 7 points apiece with St Paul's of Bessbrook at Drumragh.
At half time St Eunan's lead 4-2 but the Armagh college out scored them in the second half to force a draw.
The equalising point for St Paul's came with the final kick of the game.
Niall O’Donnell scored 0-3 for St Eunan's while Rory Carr hit 0-2 for Gary McDaid's side.
St Eunan's will play St Colmans of Newry next week.