Ryan O’Kane had Sligo ahead in the first half, with Sligo academy graduate Paul Doyle scoring against his former side in the second-half to bring the sides level.
Sligo’s FAI Cup shock defeat to Kerry FC will go down in history as one of the club’s worst results, and manager John Russell urged his players to use their disappointment as fuel going into an important stage of the season.
Kevin Doherty, too, was looking for a reaction after his side were beaten on penalties by Shamrock Rovers in the semi-final last week.
The home side had the best of the chances early on, with Elding striking the crossbar after 11 minutes.
The 19-year-old was one-on-one with Luke Dennison on 25 minutes but the Drogheda goalkeeper made himself big, with Elding unable to direct his effort around the American.
Seb Quirk forced another save from Dennison on 29 minutes, before Kevin Doherty’s side enjoyed their own spell of dominance.
A misplaced backpass from John Mahon was nicely placed for the onrushing Darragh Markey, with a double save from Sargeant denying the visitors an opener with Ryan Brennan, who came on after 34 minutes, almost firing the follow-up into the net.
A brilliant strike from Conor Keeley just skimmed the left hand post, as the hosts breathed a sigh of relief.
The opener arrived in additional time, when Russell’s men went on the counter attack.
Elding spotted the run of O’Kane to his left, and the Shels loanee cut inside and struck into the bottom left corner as Dennison was stretching.
Kevin Doherty made three changes at half-time, and those changes brought a new energy to the visitors who looked a lot more dangerous after the break.
They were back level five minutes into the half, when Paddy McClean handled the ball in the box, with Doyle scoring against his former side from the penalty spot as he sent Sargeant the wrong way.
Jad Hakiki hit the crossbar 20 minutes into the second half, as close as either side would come to finding a winner in a scrappy game.
On a night of 1-1 draws, the result changes little in terms of the table for either side.
Sligo Rovers: S Sargeant, E Agbaje (Wolfe, 78), J Mahon, P McClean, S Stewart (C Kavanagh, 62), J McManus (C Reynolds 88), S Quirk, J Hakiki, R O’Kane, W Fitzgerald, O Elding.
Drogheda United: L Dennison, O Lambe, A Quinn, C Keeley, J Bolger (F Cooper 66)), C Kane (K Cruise HT, L Heeney, P Doyle (T Oluwa 76), D Markey (D Kareem HT), W Davis (Farell HT), J Thomas (R Brennan, 34).
Referee: M Lynch