Dave Mooney took his goals tally to 13 for the season as Cork strolled into the eircom League Cup semi-finals at United Park.
Both teams fielded strong line-ups, with Drogheda showing just two changes from the side that defeated Galway and want-away George O'Callaghan Cork's only notable absentee.
The Leesiders dominated the early exchanges and both Dan Murray and Denis Behan wasted early headed chances, but Drogheda almost hit the front when Sami Ristila’s deflected shot crashed off the crossbar.
Alan Mathews' men deservedly struck on the half-hour, however, when Denis Behan pounced on a mistake by Stuart Byrne before teeing up Dave Mooney who fired decisively into the top corner of the net from just inside the box.
Colin Healy almost doubled Cork's advantage just before half time when his curling free kick was well saved by Jamie Ewings in the Drogheda goal, and Liam Kearney blazed over the bar straight after the restart.
But it took a goal-line clearance from Dan Murray to deny Adam Hughes an equaliser for the Drogs, after the Australian midfielder latched onto Joe Kendrick’s low cross.
Murray then popped up at the other end with a powerful header which Ewings saved with his feet.
Drogheda rarely threatened the Leesiders' goal, however, and it was no surprise when the visitors doubled their lead 10 minutes from time. Mooney won a free kick on the edge of the box and his kick beat Ewings with the help of a deflection off the defensive wall.
Drogheda United: Ewings, Gavin, Tambouras, Maher, Kendrick, Ristila, Hughes, Byrne, Keegan, Cahill, O'Keeffe.
Substitutes: Robinson for Cahill (52min), Bates for Ristila (65min), Iyane Thiam for O'Keeffe (82min).
Cork City: Devine, Horgan, Sullivan, Murray, Danny Murphy, Darren Murphy, Gamble, Healy, Kearney, Mooney, Behan. Substitute: O'Flynn for Behan (90min).
Referee: Richie Winter (Dublin)
