The visitors took a deserved lead after just four minutes when a left-sided cross from Colin T O'Brien was headed home by the well-placed Kevin Doyle in the Derry penalty area.
Ciaran Martyn slammed a potential equaliser against the Cork crossbar whilst captain Eamonn Doherty forced keeper Michael Devine to make a smart save in the Cork goal just before the break.
Cork had George O'Callaghan sent off on 50 minutes for retaliation on Eddie McCallion, his second bookable offence, allowing second-from-bottom Derry back into the game.
Michael Holt then levelled for Derry on 62 minutes when drilling home from the edge of the area from Gareth McGlynn's corner.