The swapping of goals by Ryan McEvoy and Alan McNally shortly before half-time offered the promise of more to come in an open encounter at Dalymount.
But try as both sides might, they had to settle for a point from a game either of them could have won.
Determined to put in a better display than on their last home showing in defeat to Monaghan, Bohs started the brighter, with Luke Byrne venturing forward from left-back to loop a header off the bar from Keith Ward’s cross
Drogheda’s impressive start to the season has stuttered of late and they came into the game with just one win in four games.
But with Brennan brothers, Ryan and Gavin, back in the side following illness, Mick Cooke’s men slowly worked their way into the match to create their first opening on 23 minutes; Declan O’Brien flicking just over the top from Eric Foley’s delivery from the left.
O’Brien was there again soon after to work Mark McNulty in the Bohemians goal with a glancing header from Stephen Quigley’s cross from the right.
The guile of O’Brien brought another chance on 32 minutes, this time the striker’s first-time shot veering just over the bar from Peter Hynes’ through ball.
But it was Bohemians who snatched the lead from a corner on 38 minutes.
Keith Ward played it short to Keith Buckley, his attempted cross was deflected away to the lurking McEvoy whose left-foot volley from just outside the box bounced past keeper Gabriel Sava and into the corner of the net.
Drogheda were back level within two minutes from a poorly defended corner at the other end. Foley’s delivery was only half-cleared and captain McNally drilled a shot home through a crowded goalmouth.
The introduction of Paul Crowley, who took the armband from McNally, gave Drogheda a driving force in midfield and he shot narrowly wide minutes into the second half.
But it needed a brilliant tip-over save from Sava to prevent Bohemians regaining the lead on 58 minutes when Byrne again got his head to a Ward corner.
Bohemians substitute keeper Craig Sexton proved his worth too, with a super reflex stop with his feet form a Derek Prendergast header 20 minutes from the end.
Both sides finished strongly, with Drogheda’s Sean Brennan having a shot blocked in a crowded box on 88 minutes the closest either side came to snatching a winner.
BOHEMIANS: McNulty (Sexton 55); Pender, McMillan, Feely, L Byrne; Traynor; Buckley, Ward (Mulcahy 65), McEvoy, McMahon (Moore 81); Corcoran.
DROGHEDA UNITED: Sava; Quigley (Crowley 36), Prendergast, McNally, Grimes; Gannon, Foley, R Brennan, G Brennan; Hynes (Mulvenna 83), D O’Brien (S Brennan 69).
Referee: Anthony Buttimer (Cork).
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