A late surge from the Oak Leafers wasn’t enough as Cork edged to a two-point win at Páirc Uí Chaoimh.
Goals from Shane McGuigan and Niall Loughlin helped Derry to a four-point victory over Louth in Round 4.
Shane McGuigan notched 0-7 for Derry as they claimed their first victory of the league campaign.
Down finished strongest at Pairc Esler on Saturday night as Derry fell to a disappointing late defeat.
Ciaran McFaul’s late point rescued a draw for Derry against Leitrim in the Division 3 opener at Celtic Park.
Donegal overcame Derry by five points in an uninspiring Round 3 McKenna Cup fixture at Celtic Park on Wednesday night.