Mick Cooke's side scored five minutes from time to set up a replay in their FAI Cup quarter-final after Ciaran Coll was sent off for the Airtricity First Division side
An entertaining opening saw both sides create good chances in the first few minutes. Drogs forced an early corner after Alan Byrne's header was cleared to safety, while Damien McNulty called Michael Schilgermann into action at the other end. Ryan Brennan and Gavin Brennan both had efforts at goal for the visitors, but it was the Airtricity First Division side who took the lead, with Kevin McHugh scoring his 170th goal for Harps with a fine effort from just inside the area.
Ciaran Coll went close to doubling Harps' lead moments later, while Pat McCann was denied by Schlingermann as the hosts grew in confidence after the goal. Drogs showed signs of improvement after the break, and were given a lifeline just before the hour mark when Coll was dismissed for an off-the-ball incident.
Drogheda pushed more players forward after the red card, and saw Declan O'Brien and Jason Marks both spurn good chances, but the Airtricity Premier Division side finally got the equaliser in the 85th minute as Michael Daly struck from David Cassidy's cross.
Drogheda United will now host Finn Harps at Hunky Dorys Park on Monday, September 16 in the replay, with the winner progressing to the FAI Cup semi-final.