DECLAN O'BRIEN converted an 87th-minute penalty to break Cork City's hearts at Hunky Dorys Park.
The Boynesiders made the better start and Ryan Brennan created an opening for Graham Rusk, whose mis-hit shot looped over goalkeeper Mark McNulty and off the crossbar before being scrambled clear by the Cork defence.
Drogheda skipper Derek Prendergast then wasted a great chance on 32 minutes when he headed the ball over from inside the six-yard box and the home team were made to pay 60 seconds later when Shane Duggan rifled home a shot from almost 30 yards after his initial effort was blocked.
The Leesiders looked like they would hang on for the points until referee Neil Doyle harshly penalised a defender for handball in the box and O'Brien fired home the resulting penalty kick.
DROGHEDA UTD – Sava; Quigley, Gannon, Prendergast, Grimes; Cassidy, Rusk (G Brennan 46), O'Conor, Foley (Hynes 69), R Brennan; O'Neill (O'Brien 69).
CORK CITY – McNulty; Dunleavy, Spillane, K Murray (Buckley 25), Murphy; Morrissey, Healy, Duggan, Rundle (Turner 58); Furlong (Kavanagh 90), Behan.
Ref – N Doyle (Dublin)