Derek Prendergast got his marching orders in the 20th minute for a second bookable offence when the foul seemed to be committed by teammate Lorcan Fitzgerald. It saw the game explode into life.
Bohs managed to frustrate the home side before striking right at the death through former Dundalk striker Marc Griffin.
And when Bohs conceded a penalty in another controversial moment in stoppage time, it seemed that Drogheda would get their noses in front. Anto Murphy got a yellow for the innocuous tackle on Stephen Maher in the box, but Delany dived to his right to save Daryl Kavanagh’s tame spot kick.
Drogheda had almost taken the lead on 87 minutes when Delany was caught off his line but Lee Duffy’s chip was cleared onto the bar by Lorcan Fitzgerald.
And a minute later, Bohs broke and Griffin chipped over the exposed Micheal Schlingermann in the Drogheda goal.
Schlingermann; Daly, Buckley, Byrne, Gorman; Brady, Hughes, Maher, Scott; Duffy, Kavanagh.
Brennan for Scott (56min), Dunne for Hughes (68min).
Delany; Pender, Prendergast, Murphy, Fitzgerald, Kavanagh, Buckley, Creevy, Lopes, Evans, Kelly.
Griffin for Kelly (78min), Dillon for Evans (85min).
Paul McLaughlin (Monaghan).