Jesse Devers rescued a point in the 91st minute for Galway United in a frantic finish – barely 60 seconds after Adam Wixted had put Drogheda ahead for the second time.
Drogheda started the game on the front foot and Galway keeper Conor Winn was called into action inside the first minute to beat away a close-range effort by Jake Hyland.
Stephen Elliott almost profited from some hesitant defending from the visitors in the eighth minute and so it was no surprise when the Boynesiders took the lead from their next attack.
Hyland was the creator as he broke from inside his own half before squaring to the onrushing Adam Wixted whose speculative 25-yard shot nestled in the net, with Winn rooted to the spot.
Galway’s first scoring opportunity arrived on 14 minutes when Ronan Murray was fouled just outside the box and Stephen Folan’s well-struck free kick was held at the second attempt by Drogs keeper Stephen McGuinness.
That marked the start of a good spell for the Tribesmen and McGuinness did well to hold a Murray shot from just inside the box in the 22nd minute.
It was end to end football at this stage and Gavin Brennan arrived late to volley wide from a Shane Elworthy cross on 26 minutes as Drogheda looked to double their advantage.
Galway remained a threat from set pieces, though, and Folan should have done better with a close-range header from a Mark Ludden corner before Marc Griffin ended the first half by shooting wide from eight yards for the Boynesiders.
Drogheda had a lucky escape straight after the restart when Folan inadvertently blocked team-mate Lee Grace’s header on the line.
Both keepers were then called into action in the space of a minute, Wixted’s snap shot held low down by Winn before McGuinness beat away Gavan Holohan’s fierce effort for the visitors.
Galway were inches away from an equaliser on 67 minutes when Murray curled a shot beyond McGuinness but just wide of the upright.
Drogheda also had a shout for a penalty when their teenage left-back Conor Kane swapped passes with Marc Griffin before going down in the box under pressure from Grace.
The visitors’s patience was finally rewarded in the 82nd minute when Cunningham sprinted clear of his marker and rifled an unstoppable shot past McGuinness.
Drogheda thought they had won it on 90 minutes when Wixted rifled home from a Gavin Brennan assist, but less than a minute later Devers broke the Boynesiders’ hearts by making it 2-2.
DROGHEDA UNITED: Stephen McGuinness; Shane Elworthy, Luke Gallagher, Ciaran McGuigan, Conor Kane; Adam Wixted, Jake Hyland, Richie Purdy, Gavin Brennan; Stephen Elliott (Sean Brennan 73), Marc Griffin (Gareth McCaffrey 73). Subs not used: Stephen Dunne, Kevin Farragher, Jamie Hollywood, Ryan Coulter.
GALWAY UNITED: Conor Winn; Colm Horgan, Stephen Folan, Lee Grace, Mark Ludden; Gary Shanahan (Conor Melody 69), Gavan Holohan, David Cawley, Kevin Devaney; Ronan Murray (Jesse Devers 88), Vinny Faherty (Padraic Cunningham 69). Subs not used: Alex Byrne, Paul Sinnott, Aaron Conway, Ciaran Nugent.
Referee: Jim McKell (Tipperary)