The Mournemen led 0-9 to 0-3 at half-time but Antrim hit back in style to edge ahead on 62 minutes.
However, a superb move involving Danny Hughes, Benny Coulter and Martin Clarke ended with Aidan Carr firing over the equaliser two minutes from time.
Both sides had been reduced to 14 men early in the second half as James Colgan and Tomas McCann got straight red cards.
ANTRIM: S O’Neill; C Brady, A McLean, K O’Boyle; T Scullion, J Crozier, T O’Neill; B Herron, A Gallagher; D O’Neill, J Laverty, M McAleese; P Cunningham (0-9, 7f), K Niblock (0-1), E McNeill.
Subs: M Dougan (0-1) for E McNeill, T McCann for J Laverty, M Sweeney (0-1) for M McAleese, R Johnston for K Niblock, A Healy for T Scullion.
DOWN: G Joyce; P McPolin, G McArdle, K Duffin; K Anderson, J Colgan, K McKernan (0-1); P Fitzpatrick (0-1), M Magee (0-1); D Hughes (0-2), A Carr (0-2), C Maginn; C Laverty (0-1), R Murtagh, M Clarke (0-4, 2f).
Subs: J Clarke for R Murtagh, B Coulter for C Laverty, M Doran for K Anderson, D McCartan for K Duffin, D Gordon for C Maginn
Referee: M Higgins (Fermanagh)