Bohemians kept their European hopes alive with a 79th minute header from Tony O'Connor which gave them the points at Dalymount Park last night.
Drogheda, however, had struck first when John Coady converted from the penalty spot after David Fairclough had upended Noel Reid.
Bohemians, though, began to press and struck before the interval when a free from the right was met by the head of Maurice O'Driscoll.
The Drogheda goal lived a charmed existence after the interval with both O'Connor and O'Driscoll hitting the woodwork.
Finally, with 11 minutes to go, Bohemians secured victory when O'Connor headed in at the near post following a Derek Swan free kick.
Bohemians: Dempsey, Broughan, Fairclough, Mullen, O'Driscoll, Byrne, Mooney, O'Connor, Swan, Lawlor, McGrath. Subs: Doolin for Fairclough (half-time); Ryan for McGrath (76 mins).
Drogheda United: Byrne, Hill, Quinn, Impey, Carroll, Coady, Ramage, O'Dowd, Nigel Reid, John Reid, R Fox. Subs: Kelly for O'Dowd, Murphy for Carroll, Brennan for Quinn (all half-time).
Referee: J Casey (Waterford).