Cork made it five wins from five but were almost caught by a late Derry fightback at Páirc Uí Chaoimh yesterday.
Before a crowd of 1,874, Cork led by four points (1-5 to 0-4) at the break after playing with the wind and eased clear in the second period, aided by two goals from John O'Rourke.
When sub Michael Hurley pointed in the 63rd minute the Rebels were 3-12 to 1-8 clear.
However, Derry didn't give up and Shane McGuigan's fourth point was followed by a goal from Emmett Bradley, just after Cork goalkeeper Anthony Casey had denied sub Declan Cassidy. Though another McGuigan free was answered by a Damien Gore point and Derry needed a goal-line clearance to deny Ian Maguire, the deficit was down to three after Niall Keenan set up Patrick Kearney for a goal in the second of four minutes of injury-time.
McGuigan cut the gap further and Derry had a last chance when Carlus McWilliams sent a ball goalwards but Mattie Taylor came away with possession and the Rebels held out. Defending deep against the wind in the first half, Derry fell behind as Cork played smartly. It was 1-3 to 0-1 for the hosts when Gore capitalised on a mix-up to goal in the 18th minute.
Goalkeeper Odhrán Lynch (45), Bradley and McWilliams helped Derry to come to within four by the break, but Cork looked to have pulled clear as sub Cathail O'Mahony made a good contribution with points and O'Rourke fired in two goals.
Scorers - Cork: J O'Rourke 2-2 (0-1m); D Gore 1-3 (0-1m); C O'Mahony 0-4 (2f); L Connolly 0-2 (1f); E McSweeney, M Hurley 0-1 each. Derry: S McGuigan 0-6 (6f); E Bradley, N Loughlin (1f) 1-1 each; P Kearney 1-0; P Cassidy, C McWilliams (m), O Lynch (45) 0-1 each.
CORK - A Casey 6; T Clancy 6, M Shanley 7, P Ring 6; L O'Donovan 6, S Powter 8, M Taylor 7; I Maguire 7, K O'Hanlon 8; J O'Rourke 8, S White 6, B Hartnett 6; P Kerrigan 7, L Connolly 7, D Gore 8. Subs: C O'Mahony 8 for Connolly (inj, 26), K O'Donovan 7 for L O'Donovan (inj, 35), E McSweeney 6 for Hartnett (45), M Hurley for Kerrigan (62), J Loughrey for Powter (64).
DERRY - O Lynch 6; P McGrogan 6, B Rogers 6, C McWilliams 7; S Downey 7, C McKaigue 6, N Keenan 7; C McFaul 6, P Cassidy 6; E Bradley 7, N Loughlin 7, D Tallon 6; B Heron 6, S McGuigan 7, N Toner 6. Subs: L McGoldrick 6 for Cassidy (43), P Kearney 7 for Toner (43), C Doherty 6 for Tallon (57), D Cassidy for Heron (62).
REF - F Kelly (Longford)