However, the Leesiders were pushed all the way by a determined Drogheda side and the home side could consider themselves unlucky not to claim at least a share of the points.
Drogheda caretaker boss Darius Kierans named an unchanged starting XI following last week’s win in Bray, while the Leesiders had Josh O’Shea, Dave O’Leary and Gavin Kavanagh in for the suspended Dan Murray, injured Iarfhlaith Davoren and Cillian Morrison who was named alongside John O’Flynn on the subs’ bench.
Cork boss John Caulfield had referred to the relatively narrow pitch at United Park in the build-up to this match and the opening exchanges were, not surprisingly, tight, although the home side forced three corners in quick succession.
In the 10th minute Billy Dennehy tested Micheal Schlingermann from distance, but the keeper seemed to be beaten on the quarter-hour mark when Darren Dennehy’s 35-yard piledriver grazed the outside of a post.
Drogheda immediately counter-attacked through Carl Walshe and the ball eventually reached Gavin Brennan whose shot was blocked by Darren Dennehy.
Action swung back to the other end and the two Dennehys threatened for a second time, with centre-half Darren’s long-range effort requiring a superb tip-over save from Schlingermann.
Mark O’Sullivan was being well marshalled and Drogheda, with their confidence clearly boosted by last week’s win, were growing into the game.
Cork netminder Mark McNulty had to be on his toes to keep out a Brennan effort just after the half-hour and the hosts also had a shout for a penalty when Holohan went down as he was challenged by Colin Healy.
McNulty also needed two attempts to deal with a Brennan header as Drogheda finished the half strongly.
But Cork should have gone ahead on 51 minutes when Liam Kearney, just on as a sub for Gavin Kavanagh, escaped from his marker and delivered the perfect cross for Josh O’Shea whose volley rose over the bar from 12 yards.
Then it was the Cork goal’s turn to lead a charmed life as Gary O’Neill squared into the path of Holohan whose 30-yard drive rattled the crossbar.
Caulfield had emptied his bench by the 67th minute, adding extra firepower in Cillian Morrison and then John O’Flynn in a bid to unlock a well-drilled Drogheda defence, while the Boynesiders brought on fresh legs in Declan O’Brien and Sean O’Connor.
Cork should have struck on 81 minutes when O’Flynn attempted to set up a team-mate when better placed to score himself, but Drogheda couldn’t clear their lines and moments later Garry Buckley lashed the ball past Schlingermann for the crucial lead goal.
Drogheda pushed hard for an equalising goal but found Cork in no mood to surrender their proud record of clean sheets, which now extends to seven matches.
Schlingermann; Doyle, McNally, Daly, Grimes; Brady, Maher, Holohan, Brennan, Walshe; O’Neill. Subs: S O’Connor for Brady (73min), O’Brien for O’Neill (74min).
McNulty; Lenihan, G Kavanagh, D Dennehy, Dunleavy; B Dennehy, Healy, Buckley, O’Leary O’Shea; O’Sullivan. Subs: Kearney for Kavanagh (51min), Morrison for O’Shea (59min), O’Flynn for O’Leary (67min).
Rob Rogers (Dublin).